Fractional calculus is widely used to deal with nonconservative dynamics because of its memorability and non-local properties.In this paper,the Herglotz principle with generalized operators is discussed,and the Herglo...Fractional calculus is widely used to deal with nonconservative dynamics because of its memorability and non-local properties.In this paper,the Herglotz principle with generalized operators is discussed,and the Herglotz type equations for nonholonomic systems are established.Then,the Noether symmetries are studied,and the conserved quantities are obtained.The results are extended to nonholonomic canonical systems,and the Herglotz type canonical equations and the Noether theorems are obtained.Two examples are provided to demonstrate the validity of the methods and results.展开更多
In this paper, we introduce the generalized R oper-Suffridge extension operator for locally biholomorphic mappings. It is sh own that this operator preserves the starlikeness on some Reinhardt domains and does not pre...In this paper, we introduce the generalized R oper-Suffridge extension operator for locally biholomorphic mappings. It is sh own that this operator preserves the starlikeness on some Reinhardt domains and does not preserve convexity for some cases. Meanwhile, the growth theorem and di stortion theorem of the corresponding mappings are given.展开更多
In the article we consider the fractional maximal operator Mα, 0 ≤α 〈 Q on any Carnot group G （i.e., nilpotent stratified Lie group） in the generalized Morrey spaces Mp,φ（G）, where Q is the homogeneous dimens...In the article we consider the fractional maximal operator Mα, 0 ≤α 〈 Q on any Carnot group G （i.e., nilpotent stratified Lie group） in the generalized Morrey spaces Mp,φ（G）, where Q is the homogeneous dimension of G. We find the conditions on the pair （φ1, φ2） which ensures the boundedness of the operator Ms from one generalized Morrey space Mp,φ1 （G） to another Mq,φ2 （G）, 1. 〈 p ≤q 〈 ∞. 1/p - 1/q = α/Q, and from the space M1,φ1 （G） to the weak space Wq,φ2 （G）, 1 〈 q 〈 ∞, 1 - 1/q = α/Q. Also find conditions on the φ which ensure the Adams type boundedness of the Ms from M α （G） from Mp,φ^1/p（G）to Mq,φ^1/q（G） for 1 〈p〈q〈∞ and fromM1,φ（G） toWMq,φ^1/q（G）for 1〈q〈∞. In the case b ∈ BMO（G） and 1 〈 p 〈 q 〈 ∞, find the sufficient conditions on the pair （φ1, φ2） which ensures the boundedness of the kth-order commutator operator Mb,α,k from Mp,φ1 （G） to Mq,φ2（G） with 1/p - 1/q = α/Q. Also find the sufficient conditions on the φ which ensures the boundedness of the operator Mb,α,k from Mp,φ^1/p（G） tom Mp,φ^1/p （G） for 1 〈p〈q〈∞. In all the cases the conditions for the boundedness of Mα are given it terms of supremaltype inequalities on （φ1, φ2） and φ , which do not assume any assumption on monotonicity of （φ1, φ2） and φ in r. As applications we consider the SchrSdinger operator -△G ＋ V on G, where the nonnegative potential V belongs to the reverse Holder class B∞（G）. The MB,φ1 - Mq,φ2 estimates for the operators V^γ（-△G ＋ V）^-β and V^γ△↓G（-△G ＋ V）^-β are obtained.展开更多
The relation between generalized operators and operator-valued distributions is discussed so that these two viewpoints can be used alternatively to explain quantum fields.
Compared with the Hamiltonian mechanics and the Lagrangian mechanics,the Birkhoffian mechanics is more general.The Birkhoffian mechanics is discussed on the basis of the generalized fractional operators,which are prop...Compared with the Hamiltonian mechanics and the Lagrangian mechanics,the Birkhoffian mechanics is more general.The Birkhoffian mechanics is discussed on the basis of the generalized fractional operators,which are proposed recently.Therefore,differential equations of motion within generalized fractional operators are established.Then,in order to find the solutions to the differential equations,Noether symmetry,conserved quantity,perturbation to Noether symmetry and adiabatic invariant are investigated.In the end,two applications are given to illustrate the methods and results.展开更多
By extending the usual Wigner operator to the s-parameterized one as 1/4π2 integral （dyduexp [iu（q-Q）＋iy（p-P）＋is/2yu]） from n=- ∞ to ∞ with s beng a,real parameter,we propose a generalized Weyl quantization...By extending the usual Wigner operator to the s-parameterized one as 1/4π2 integral （dyduexp [iu（q-Q）＋iy（p-P）＋is/2yu]） from n=- ∞ to ∞ with s beng a,real parameter,we propose a generalized Weyl quantization scheme which accompanies a new generalized s-parameterized ordering rule.This rule recovers P-Q ordering,Q-P ordering,and Weyl ordering of operators in s = 1,1,0 respectively.Hence it differs from the Cahill-Glaubers’ ordering rule which unifies normal ordering,antinormal ordering,and Weyl ordering.We also show that in this scheme the s-parameter plays the role of correlation between two quadratures Q and P.The formula that can rearrange a given operator into its new s-parameterized ordering is presented.展开更多
In this paper by Sobolev imbedding theorem and characterization theorem of generalized operators the existence of P(φ)2 quantum fields as generalized operators is obtained and a rigorous mathematical interpretation o...In this paper by Sobolev imbedding theorem and characterization theorem of generalized operators the existence of P(φ)2 quantum fields as generalized operators is obtained and a rigorous mathematical interpretation of renormalization procedure is given under white noise theory.展开更多
Let G be a homogeneous group. The author considers the boundedness of commutators generated by the generalized Hardy operators and CMO（G） functions on Herz spaces in the setting of homogeneous group. This article ex...Let G be a homogeneous group. The author considers the boundedness of commutators generated by the generalized Hardy operators and CMO（G） functions on Herz spaces in the setting of homogeneous group. This article extends some known results.展开更多
Suppose f is an almost starlike function of order α on the unit disk D. In this paper, we will prove that Фn,β2,γ2,…βn,γn（f）（z）=（f（z1）,（f（z1）/z1）^β2（f＇（z1））^γ2 z2,…,（f（z1）/z1）^βn（f＇（z...Suppose f is an almost starlike function of order α on the unit disk D. In this paper, we will prove that Фn,β2,γ2,…βn,γn（f）（z）=（f（z1）,（f（z1）/z1）^β2（f＇（z1））^γ2 z2,…,（f（z1）/z1）^βn（f＇（z1））^γnzn）1 preserves almost starlikeness of order α on Ωn,p2,…,pn={z=（z1,z2,…,zn）＇∈Cn：∑^n j=1｜zj｜^pj〈1},where 0〈p1≤2,pj≥1,j=2,…,n,are real numbers.展开更多
In this paper, by the definition of spirallike mapping of type β and order α ,we discuss that the generalized Roper-Suffridge extension operator preserves spirallikeness of type β and order α in complex Banach spa...In this paper, by the definition of spirallike mapping of type β and order α ,we discuss that the generalized Roper-Suffridge extension operator preserves spirallikeness of type β and order α in complex Banach spaces.展开更多
In this paper, we introduce some new subclasses of meromorphically uniformly reciprocal starlike functions associated with the generalized Dziok-Srivastava operator and its corresponding integral operator defined by s...In this paper, we introduce some new subclasses of meromorphically uniformly reciprocal starlike functions associated with the generalized Dziok-Srivastava operator and its corresponding integral operator defined by subordination. We obtain the inclusion relation, sufficient conditions and raajorization property of the class. Moreover, we point out some new and interesting corollaries of our main result. These results generalize some known results.展开更多
Littlewood-Paley operators and Marcinkiewicz integral on generalized Campanula spaces ερ,φ are studied. It is proved that the image of a function under the action of these operators is either equal to infinity almo...Littlewood-Paley operators and Marcinkiewicz integral on generalized Campanula spaces ερ,φ are studied. It is proved that the image of a function under the action of these operators is either equal to infinity almost everywhere or is in ερ,φ.展开更多
In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green fun...In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green function about the operators is also given.展开更多
Based on the displacement-squeezing related squeezed coherent state representation ｜z〉g and using the technique of integration within an ordered product of operators, this paper finds a generalized Fresnel operator,...Based on the displacement-squeezing related squeezed coherent state representation ｜z〉g and using the technique of integration within an ordered product of operators, this paper finds a generalized Fresnel operator, whose matrix element in the coordinate representation leads to a generalized Collins formula （Huygens-Fresnel integration transformation describing optical diffraction）. The generalized Fresnel operator is derived by a quantum mechanical mapping from z to sz -- rz^＊ in the ｜Z〉g representation, while ｜z〉g in phase space is graphically denoted by an ellipse.展开更多
Based on the generalized Weyl quantization scheme, which relies on the generalized Wigner operator Ok （p, q） with a real k parameter and can unify the P-Q, Q-P, and Weyl ordering of operators in k = 1, - 1,0, respec...Based on the generalized Weyl quantization scheme, which relies on the generalized Wigner operator Ok （p, q） with a real k parameter and can unify the P-Q, Q-P, and Weyl ordering of operators in k = 1, - 1,0, respectively, we find the mutual transformations between 6 （p - P） （q - Q）, （q - Q） 3 （p - P）, and （p, q）, which are, respectively, the integration kernels of the P-Q, Q-P, and generalized Weyl quantization schemes. The mutual transformations provide us with a new approach to deriving the Wigner function of quantum states. The - and - ordered forms of （p, q） are also derived, which helps us to put the operators into their - and - ordering, respectively.展开更多
In this paper, we introduce the class of n-normed generalized difference sequences related to lp-space. Some properties of this sequence space like solidness, symmetricity, convergence-free etc. are studied. We obtain...In this paper, we introduce the class of n-normed generalized difference sequences related to lp-space. Some properties of this sequence space like solidness, symmetricity, convergence-free etc. are studied. We obtain some inclusion relations involving this sequence space.展开更多
Generalized morphological operator can generate less statistical bias in the output than classical morphological operator. Comprehensive utilization of spectral and spatial information of pixels, an endmember extracti...Generalized morphological operator can generate less statistical bias in the output than classical morphological operator. Comprehensive utilization of spectral and spatial information of pixels, an endmember extraction algorithm based on generalized morphology is proposed. For the limitations of morphological operator in the pixel arrangement rule and replacement criteria, the reference pixel is introduced. In order to avoid the cross substitution phenomenon at the boundary of different object categories in the image, an endmember is extracted by calculating the generalized opening-closing(GOC) operator which uses the modified energy function as a distance measure. The algorithm is verified by using simulated data and real data. Experimental results show that the proposed algorithm can extract endmember automatically without prior knowledge and achieve relatively high extraction accuracy.展开更多
We construct the nonlinear tripartite entangled state representation and the related generalized Wigner operator. Then we discussed the Wigner functions of the nonlinear tripartite entangled state and the three-mode n...We construct the nonlinear tripartite entangled state representation and the related generalized Wigner operator. Then we discussed the Wigner functions of the nonlinear tripartite entangled state and the three-mode nonlinear squeezed vacuum state, and obtained the classical Weyl corresponding function of the three-mode nonlinear squeezed state.展开更多
Let f be a holomorphic function on the unit polydisc Dn,with Taylor expansion f(z) = ∞ |k|=0 akzk ≡ ∞ (k1+···+kn=0) (ak1,···,kn zk1 1znkn)where k = (k1, , kn) ∈ Z+n. The authors defin...Let f be a holomorphic function on the unit polydisc Dn,with Taylor expansion f(z) = ∞ |k|=0 akzk ≡ ∞ (k1+···+kn=0) (ak1,···,kn zk1 1znkn)where k = (k1, , kn) ∈ Z+n. The authors define generalized Hilbert operator on Dn by Hγ,n(f)(z) = ∞ |k|=0 i1,···,in≥0 ai1,···,in n j=1 Γ(γj + kj + 1)Γ(kj + ij + 1) Γ(kj + 1)Γ(kj + ij + γj + 2) zk,where γ ∈ Cn, such that R γj > -1, j = 1, 2, , n. An upper bound for the norm of the operator on Hardy spaces Hp(Dn) is found. The authors also present a Fejér-Riesz type ineq...展开更多
The object of this article is to study and develop the generalized fractional calcu- lus operators given by Saigo and Maeda in 1996. We establish generalized fractional calculus formulas involving the product of R-fun...The object of this article is to study and develop the generalized fractional calcu- lus operators given by Saigo and Maeda in 1996. We establish generalized fractional calculus formulas involving the product of R-function, Appell function F3 and a general class of poly- nomials. The results obtained provide unification and extension of the results given by Saxena et al. [13], Srivastava and Grag [17], Srivastava et al. [20], and etc. The results are obtained in compact form and are useful in preparing some tables of operators of fractional calculus. On account of the general nature of the Saigo-Maeda operators, R-function, and a general class of polynomials a large number of new and known results involving Saigo fractional calculus operators and several special functions notably H-function, /-function, Mittag-Leffier function, generalized Wright hypergeometric function, generalized Bessel-Maitland function follow as special cases of our main findings.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12272248)the Postgraduate Research and Practice Innovation Program of Jiangsu Province of China(Grant No.KYCX23_3296).
文摘Fractional calculus is widely used to deal with nonconservative dynamics because of its memorability and non-local properties.In this paper,the Herglotz principle with generalized operators is discussed,and the Herglotz type equations for nonholonomic systems are established.Then,the Noether symmetries are studied,and the conserved quantities are obtained.The results are extended to nonholonomic canonical systems,and the Herglotz type canonical equations and the Noether theorems are obtained.Two examples are provided to demonstrate the validity of the methods and results.
文摘In this paper, we introduce the generalized R oper-Suffridge extension operator for locally biholomorphic mappings. It is sh own that this operator preserves the starlikeness on some Reinhardt domains and does not preserve convexity for some cases. Meanwhile, the growth theorem and di stortion theorem of the corresponding mappings are given.
基金partially supported by the grant of Ahi Evran University Scientific Research Projects(FEN 4001.12.0018)partially supported by the grant of Ahi Evran University Scientific Research Projects(FEN 4001.12.0019)+1 种基金by the grant of Science Development Foundation under the President of the Republic of Azerbaijan project EIF-2010-1(1)-40/06-1partially supported by the Scientific and Technological Research Council of Turkey(TUBITAK Project No:110T695)
文摘In the article we consider the fractional maximal operator Mα, 0 ≤α 〈 Q on any Carnot group G （i.e., nilpotent stratified Lie group） in the generalized Morrey spaces Mp,φ（G）, where Q is the homogeneous dimension of G. We find the conditions on the pair （φ1, φ2） which ensures the boundedness of the operator Ms from one generalized Morrey space Mp,φ1 （G） to another Mq,φ2 （G）, 1. 〈 p ≤q 〈 ∞. 1/p - 1/q = α/Q, and from the space M1,φ1 （G） to the weak space Wq,φ2 （G）, 1 〈 q 〈 ∞, 1 - 1/q = α/Q. Also find conditions on the φ which ensure the Adams type boundedness of the Ms from M α （G） from Mp,φ^1/p（G）to Mq,φ^1/q（G） for 1 〈p〈q〈∞ and fromM1,φ（G） toWMq,φ^1/q（G）for 1〈q〈∞. In the case b ∈ BMO（G） and 1 〈 p 〈 q 〈 ∞, find the sufficient conditions on the pair （φ1, φ2） which ensures the boundedness of the kth-order commutator operator Mb,α,k from Mp,φ1 （G） to Mq,φ2（G） with 1/p - 1/q = α/Q. Also find the sufficient conditions on the φ which ensures the boundedness of the operator Mb,α,k from Mp,φ^1/p（G） tom Mp,φ^1/p （G） for 1 〈p〈q〈∞. In all the cases the conditions for the boundedness of Mα are given it terms of supremaltype inequalities on （φ1, φ2） and φ , which do not assume any assumption on monotonicity of （φ1, φ2） and φ in r. As applications we consider the SchrSdinger operator -△G ＋ V on G, where the nonnegative potential V belongs to the reverse Holder class B∞（G）. The MB,φ1 - Mq,φ2 estimates for the operators V^γ（-△G ＋ V）^-β and V^γ△↓G（-△G ＋ V）^-β are obtained.
文摘The relation between generalized operators and operator-valued distributions is discussed so that these two viewpoints can be used alternatively to explain quantum fields.
基金This work was supported by the National Natural Science Foun-dation of China(Grants 11802193 and 11972241)the Natural Sci-ence Foundation of Jiangsu Province(Grant BK20191454)the Young Scientific and Technological Talents Promotion Project of Suzhou Association for Science and Technology.
文摘Compared with the Hamiltonian mechanics and the Lagrangian mechanics,the Birkhoffian mechanics is more general.The Birkhoffian mechanics is discussed on the basis of the generalized fractional operators,which are proposed recently.Therefore,differential equations of motion within generalized fractional operators are established.Then,in order to find the solutions to the differential equations,Noether symmetry,conserved quantity,perturbation to Noether symmetry and adiabatic invariant are investigated.In the end,two applications are given to illustrate the methods and results.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11175113 and 11147009)the Natural Science Foundation of Shandong Province of China (Grant No. ZR2010AQ027)the Program of Higher Educational Science and Technology of Shandong Province,China (Grant No. J10LA15)
文摘By extending the usual Wigner operator to the s-parameterized one as 1/4π2 integral （dyduexp [iu（q-Q）＋iy（p-P）＋is/2yu]） from n=- ∞ to ∞ with s beng a,real parameter,we propose a generalized Weyl quantization scheme which accompanies a new generalized s-parameterized ordering rule.This rule recovers P-Q ordering,Q-P ordering,and Weyl ordering of operators in s = 1,1,0 respectively.Hence it differs from the Cahill-Glaubers’ ordering rule which unifies normal ordering,antinormal ordering,and Weyl ordering.We also show that in this scheme the s-parameter plays the role of correlation between two quadratures Q and P.The formula that can rearrange a given operator into its new s-parameterized ordering is presented.
基金Project supported by NSFC (10171035) and Hubei University Youth Foundation (97A012)
文摘In this paper by Sobolev imbedding theorem and characterization theorem of generalized operators the existence of P(φ)2 quantum fields as generalized operators is obtained and a rigorous mathematical interpretation of renormalization procedure is given under white noise theory.
基金Supported by Chinese Universities Scientific Fund(2009RC0703 of BUPT)the NNSF of China (10871024)
文摘Let G be a homogeneous group. The author considers the boundedness of commutators generated by the generalized Hardy operators and CMO（G） functions on Herz spaces in the setting of homogeneous group. This article extends some known results.
基金Supported by the National Natural Science Foundation of China(10626015,10571044)Supported by the Guangdong Natural Science Foundation(06301315)+1 种基金Supported by the Doctoral Foundation of Zhanjiang Normal University(Z0420)Supported by the Natural Science Foundation of Henan University(XK03YBSX200)
文摘Suppose f is an almost starlike function of order α on the unit disk D. In this paper, we will prove that Фn,β2,γ2,…βn,γn（f）（z）=（f（z1）,（f（z1）/z1）^β2（f＇（z1））^γ2 z2,…,（f（z1）/z1）^βn（f＇（z1））^γnzn）1 preserves almost starlikeness of order α on Ωn,p2,…,pn={z=（z1,z2,…,zn）＇∈Cn：∑^n j=1｜zj｜^pj〈1},where 0〈p1≤2,pj≥1,j=2,…,n,are real numbers.
文摘In this paper, by the definition of spirallike mapping of type β and order α ,we discuss that the generalized Roper-Suffridge extension operator preserves spirallikeness of type β and order α in complex Banach spaces.
基金Supported by the National Natural Science Foundation of China(11561001)Supported by the Natural Science Foundation of Inner Mongolia Province(2014MS0101)Supported by the Higher School Foundation of Inner Mongolia Province(2015NJZY240)
文摘In this paper, we introduce some new subclasses of meromorphically uniformly reciprocal starlike functions associated with the generalized Dziok-Srivastava operator and its corresponding integral operator defined by subordination. We obtain the inclusion relation, sufficient conditions and raajorization property of the class. Moreover, we point out some new and interesting corollaries of our main result. These results generalize some known results.
文摘Littlewood-Paley operators and Marcinkiewicz integral on generalized Campanula spaces ερ,φ are studied. It is proved that the image of a function under the action of these operators is either equal to infinity almost everywhere or is in ερ,φ.
文摘In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green function about the operators is also given.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.10874174 and 10675108)the President Foundation of the Chinese Academy of Sciencesthe Specilized Research Fund for the Doctorial Program of the Higher Education of China (Grant No.20070358009)
文摘Based on the displacement-squeezing related squeezed coherent state representation ｜z〉g and using the technique of integration within an ordered product of operators, this paper finds a generalized Fresnel operator, whose matrix element in the coordinate representation leads to a generalized Collins formula （Huygens-Fresnel integration transformation describing optical diffraction）. The generalized Fresnel operator is derived by a quantum mechanical mapping from z to sz -- rz^＊ in the ｜Z〉g representation, while ｜z〉g in phase space is graphically denoted by an ellipse.
基金Project supported by the National Natural Science Foundation of China(Grant No.11175113)the Natural Science Foundation of Shandong Province of China(Grant No.Y2008A16)+1 种基金the University Experimental Technology Foundation of Shandong Province of China(Grant No.S04W138)the Natural Science Foundation of Heze University of Shandong Province of China(Grants Nos.XY07WL01 and XY08WL03)
文摘Based on the generalized Weyl quantization scheme, which relies on the generalized Wigner operator Ok （p, q） with a real k parameter and can unify the P-Q, Q-P, and Weyl ordering of operators in k = 1, - 1,0, respectively, we find the mutual transformations between 6 （p - P） （q - Q）, （q - Q） 3 （p - P）, and （p, q）, which are, respectively, the integration kernels of the P-Q, Q-P, and generalized Weyl quantization schemes. The mutual transformations provide us with a new approach to deriving the Wigner function of quantum states. The - and - ordered forms of （p, q） are also derived, which helps us to put the operators into their - and - ordering, respectively.
基金supported by the Department of Science and Technology Project No. SR/WOS-A/MS-07/2008
文摘In this paper, we introduce the class of n-normed generalized difference sequences related to lp-space. Some properties of this sequence space like solidness, symmetricity, convergence-free etc. are studied. We obtain some inclusion relations involving this sequence space.
基金supported by the National Natural Science Foundation of China(No.61275010)the PhD Programs Foundation of Ministry of Education of China(No.20132304110007)
文摘Generalized morphological operator can generate less statistical bias in the output than classical morphological operator. Comprehensive utilization of spectral and spatial information of pixels, an endmember extraction algorithm based on generalized morphology is proposed. For the limitations of morphological operator in the pixel arrangement rule and replacement criteria, the reference pixel is introduced. In order to avoid the cross substitution phenomenon at the boundary of different object categories in the image, an endmember is extracted by calculating the generalized opening-closing(GOC) operator which uses the modified energy function as a distance measure. The algorithm is verified by using simulated data and real data. Experimental results show that the proposed algorithm can extract endmember automatically without prior knowledge and achieve relatively high extraction accuracy.
基金Open Foundation of Laboratory of High-intensity Optics，中国科学院资助项目
文摘We construct the nonlinear tripartite entangled state representation and the related generalized Wigner operator. Then we discussed the Wigner functions of the nonlinear tripartite entangled state and the three-mode nonlinear squeezed vacuum state, and obtained the classical Weyl corresponding function of the three-mode nonlinear squeezed state.
基金Supported by the NNSF of China(10671115)grants from Specialized Research Fund for the doctoral program of Higher Education(20060560002)NSF of Guangdong Province(7300614)
文摘Let f be a holomorphic function on the unit polydisc Dn,with Taylor expansion f(z) = ∞ |k|=0 akzk ≡ ∞ (k1+···+kn=0) (ak1,···,kn zk1 1znkn)where k = (k1, , kn) ∈ Z+n. The authors define generalized Hilbert operator on Dn by Hγ,n(f)(z) = ∞ |k|=0 i1,···,in≥0 ai1,···,in n j=1 Γ(γj + kj + 1)Γ(kj + ij + 1) Γ(kj + 1)Γ(kj + ij + γj + 2) zk,where γ ∈ Cn, such that R γj > -1, j = 1, 2, , n. An upper bound for the norm of the operator on Hardy spaces Hp(Dn) is found. The authors also present a Fejér-Riesz type ineq...
基金NBHM Department of Atomic Energy,Government of India,Mumbai for the finanicai assistance under PDF sanction no.2/40(37)/2014/R&D-II/14131
文摘The object of this article is to study and develop the generalized fractional calcu- lus operators given by Saigo and Maeda in 1996. We establish generalized fractional calculus formulas involving the product of R-function, Appell function F3 and a general class of poly- nomials. The results obtained provide unification and extension of the results given by Saxena et al. [13], Srivastava and Grag [17], Srivastava et al. [20], and etc. The results are obtained in compact form and are useful in preparing some tables of operators of fractional calculus. On account of the general nature of the Saigo-Maeda operators, R-function, and a general class of polynomials a large number of new and known results involving Saigo fractional calculus operators and several special functions notably H-function, /-function, Mittag-Leffier function, generalized Wright hypergeometric function, generalized Bessel-Maitland function follow as special cases of our main findings.
