In this article,the multi-parameters Mittag-Leffler function is studied in detail.As a consequence,a series of novel results such as the integral representation,series representation and Mellin transform to the above ...In this article,the multi-parameters Mittag-Leffler function is studied in detail.As a consequence,a series of novel results such as the integral representation,series representation and Mellin transform to the above function,are obtained.Especially,we associate the multi-parameters Mittag-Leffler function with two special functions which are the generalized Wright hypergeometric and the Fox’s-H functions.Meanwhile,some interesting integral operators and derivative operators of this function,are also discussed.展开更多
In this paper, we use Mittag-Leffler function method for solving some nonlinear fractional differential equations. A new solution is constructed in power series. The fractional derivatives are described by Caputo'...In this paper, we use Mittag-Leffler function method for solving some nonlinear fractional differential equations. A new solution is constructed in power series. The fractional derivatives are described by Caputo's sense. To illustrate the reliability of the method, some examples are provided.展开更多
The finite-time Mittag-Leffler synchronization is investigated for fractional-order delayed memristive neural networks(FDMNN)with parameters uncertainty and discontinuous activation functions.The relevant results are ...The finite-time Mittag-Leffler synchronization is investigated for fractional-order delayed memristive neural networks(FDMNN)with parameters uncertainty and discontinuous activation functions.The relevant results are obtained under the framework of Filippov for such systems.Firstly,the novel feedback controller,which includes the discontinuous functions and time delays,is proposed to investigate such systems.Secondly,the conditions on finite-time Mittag-Leffler synchronization of FDMNN are established according to the properties of fractional-order calculus and inequality analysis technique.At the same time,the upper bound of the settling time for Mittag-Leffler synchronization is accurately estimated.In addition,by selecting the appropriate parameters of the designed controller and utilizing the comparison theorem for fractional-order systems,the global asymptotic synchronization is achieved as a corollary.Finally,a numerical example is given to indicate the correctness of the obtained conclusions.展开更多
In the present case,we propose the novel generalized fractional integral operator describing Mittag-Leffler function in their kernel with respect to another function Φ.The proposed technique is to use graceful amalga...In the present case,we propose the novel generalized fractional integral operator describing Mittag-Leffler function in their kernel with respect to another function Φ.The proposed technique is to use graceful amalgamations of the Riemann-Liouville(RL)fractional integral operator and several other fractional operators.Meanwhile,several generalizations are considered in order to demonstrate the novel variants involving a family of positive functions n(n∈N)for the proposed fractional operator.In order to confirm and demonstrate the proficiency of the characterized strategy,we analyze existing fractional integral operators in terms of classical fractional order.Meanwhile,some special cases are apprehended and the new outcomes are also illustrated.The obtained consequences illuminate that future research is easy to implement,profoundly efficient,viable,and exceptionally precise in its investigation of the behavior of non-linear differential equations of fractional order that emerge in the associated areas of science and engineering.展开更多
In the present work, a unification of certain functions of mathematical physics is proposed and its properties are studied. The proposed function unifies Lommel function, Struve function, the Bessel-Maitland function ...In the present work, a unification of certain functions of mathematical physics is proposed and its properties are studied. The proposed function unifies Lommel function, Struve function, the Bessel-Maitland function and its generalization, Dotsenko function, generalized Mittag-Leffler function etc. The properties include absolute and uniform convergence, differential recurrence relation, integral representations in the form of Euler-Beta transform, Mellin-Barnes transform, Laplace transform and Whittaker transform. The special cases namely the generalized hypergeometric function, generalized Laguerre polynomial, Fox H-function etc. are also obtained.展开更多
The principal aim of the paper is devoted to the study of some special properties of the Eα,βγ,q(Z) function for α =1/n . Authors defined the decomposition of the function Eα,βγ,q(Z) in the form of truncated po...The principal aim of the paper is devoted to the study of some special properties of the Eα,βγ,q(Z) function for α =1/n . Authors defined the decomposition of the function Eα,βγ,q(Z) in the form of truncated power series as Equations (1.7), (1.8) and their various properties including Integral representation, Derivative, Inequalities and their several special cases are obtained. Some new results are also established for the function Eα,βγ,q(Z).展开更多
In this paper, we use the Mittag-Leffler addition formula to solve the Green function of generalized time fractional diffusion equation in the whole plane and prove the convergence of the Green function.
In the paper,by making use of the principle of subordination between analytic functions with the multiplier transforms defined by generalized Mittag-Leffler function,the authors investigate subclasses of univalent ana...In the paper,by making use of the principle of subordination between analytic functions with the multiplier transforms defined by generalized Mittag-Leffler function,the authors investigate subclasses of univalent analytic functions,such as starlike functions,convex functions,close-to-convex functions and quasiconvex functions.Several inclusion relationships,inequality properties,subordination and superordination results associated with the multiplier transforms are proved and the sandwich-type results are also obtained.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
Wind turbines are continuously exposed to harsh environmental and operational conditions throughout their lifetime,leading to the gradual degradation of their components.If left unaddressed,these degraded components c...Wind turbines are continuously exposed to harsh environmental and operational conditions throughout their lifetime,leading to the gradual degradation of their components.If left unaddressed,these degraded components can adversely affect turbine performance and significantly increase the likelihood of failure.As degradation progresses,the risk of failure escalates,making it essential to implement appropriate risk control measures.One effective risk control method involves performing inspection and monitoring activities that provide valuable insights into the condition of the structure,enabling the formulation of appropriate maintenance strategies based on accurate assessments.Supervisory Control and Data Acquisition(SCADA)systems offer low-resolution condition monitoring data that can be used for fault detection,diagnosis,quantification,prognosis,and maintenance planning.One commonly used method involves predicting power generation using SCADA data and comparing it against measured power generation.Significant discrepancies between predicted and measured values can indicate suboptimal operation,natural aging,or unnatural faults.Various predictive models,including parametric and non-parametric(statistical)approaches,have been proposed for estimating power generation.However,the imperfect nature of these models introduces uncertainties in the predicted power output.Additionally,SCADA monitoring data is prone to uncertainties arising from various sources.The presence of uncertainties from these two sources-imperfect predictive models and imperfect SCADA data-introduces uncertainty in the predicted power generation.This uncertainty complicates the process of determining whether discrepancies between measured and predicted values are significant enough to warrant maintenance actions.Depending on the nature of uncertainty-aleatory,arising from inherent randomness,or epistemic,stemming from incomplete knowledge or limited data-different analytical approaches,like Probabilistic and Possibilistic,can be applied for effective management.Both,Probabilistic and Possibilistic,Approaches offer distinct advantages and limitations.The Possibilistic Approach,rooted in fuzzy set theory,is particularly well suited for addressing epistemic uncertainties,especially those caused by imprecision or sparse statistical information.This makes it especially relevant for applications such as wind turbines,where it is often challenging to construct accurate probability distribution functions for environmental parameters due to limited sensor data from hard-to-access locations.This research focuses on developing a methodology for identifying suboptimal operation in wind turbines by comparing Grid Produced Power(Measured Produced Power)with Predicted Produced Power.To achieve this,the paper introduces a Possibilistic Approach for power prediction that accounts for uncertainties stemming from both model imperfections and measurement errors in SCADA data.The methodology combines machine learning models,used to establish predictive relationships between environmental inputs and power output,with a Possibilistic Framework that represents uncertainty through possibility distribution functions based on fuzzy logic and interval analysis.A real-world case study using operational SCADA data demonstrates the approach,with XGBoost selected as the final predictive model due to its strong accuracy and computational efficiency.展开更多
A Langevin delayed fractional system with multiple delays in control,is a delayed fractional system that includes delay parameters in both state and control,is first introduced.This paper is devoted to investigating t...A Langevin delayed fractional system with multiple delays in control,is a delayed fractional system that includes delay parameters in both state and control,is first introduced.This paper is devoted to investigating the relative controllability of the Langevin delayed fractional system with multiple delays in control.For linear systems to be relatively controllable,necessary and sufficient circumstances are identified by introducing and employing the Gramian matrix.The sufficient conditions for the relative controllability of semilinear systems are ofered based on Schauder's fixed point theorem.As an unusual approach,the controllability results of the delayed system are built for the first time on the exact solution produced by the MittagLeffler type function although controllability ones in the literature are built on the Volterra integral equations or the mild solutions produced by resolvent families.展开更多
Optimizing wind energy harvesting performance remains a significant challenge.Machine learning(ML)offers a promising approach for addressing this challenge.This study proposes an ML-based approach using the radial bas...Optimizing wind energy harvesting performance remains a significant challenge.Machine learning(ML)offers a promising approach for addressing this challenge.This study proposes an ML-based approach using the radial basis function neural network(RBFNN)and differential evolution(DE)to predict and optimize the structural parameters(the diameter of the spherical bluff body D,the total spring stiffness k,and the length of the piezoelectric cantilever beam L)of the wind energy harvester(WEH).The RBFNN model is trained with theoretical data and validated with wind tunnel experimental results,achieving the coefficient-of-determination scores R2of 97.8%and 90.3%for predicting the average output power Pavgand aero-electro-mechanical efficiencyηaem,respectively.The DE algorithm is used to identify the optimal parameter combinations for wind speeds U ranging from 2.5 m/s to 6.5 m/s.The maximum Pavgis achieved when D=57.5 mm,k=28.8 N/m,L=112.1 mm,and U=4.6 m/s,while the maximumηaemis achieved when D=52.7 mm,k=29.2 N/m,L=89.2 mm,and U=4.7 m/s.Compared with that of the non-optimized structure,the WEH performance is improved by 28.6%in P_(avg)and 19.1%inη_(aem).展开更多
基金Supported by The National Undergraduate Innovation Training Program(Grant No.202310290069Z).
文摘In this article,the multi-parameters Mittag-Leffler function is studied in detail.As a consequence,a series of novel results such as the integral representation,series representation and Mellin transform to the above function,are obtained.Especially,we associate the multi-parameters Mittag-Leffler function with two special functions which are the generalized Wright hypergeometric and the Fox’s-H functions.Meanwhile,some interesting integral operators and derivative operators of this function,are also discussed.
文摘In this paper, we use Mittag-Leffler function method for solving some nonlinear fractional differential equations. A new solution is constructed in power series. The fractional derivatives are described by Caputo's sense. To illustrate the reliability of the method, some examples are provided.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61703312 and 61703313)。
文摘The finite-time Mittag-Leffler synchronization is investigated for fractional-order delayed memristive neural networks(FDMNN)with parameters uncertainty and discontinuous activation functions.The relevant results are obtained under the framework of Filippov for such systems.Firstly,the novel feedback controller,which includes the discontinuous functions and time delays,is proposed to investigate such systems.Secondly,the conditions on finite-time Mittag-Leffler synchronization of FDMNN are established according to the properties of fractional-order calculus and inequality analysis technique.At the same time,the upper bound of the settling time for Mittag-Leffler synchronization is accurately estimated.In addition,by selecting the appropriate parameters of the designed controller and utilizing the comparison theorem for fractional-order systems,the global asymptotic synchronization is achieved as a corollary.Finally,a numerical example is given to indicate the correctness of the obtained conclusions.
基金supported by the National Natural Science Foundation of China(Grant No.61673169).
文摘In the present case,we propose the novel generalized fractional integral operator describing Mittag-Leffler function in their kernel with respect to another function Φ.The proposed technique is to use graceful amalgamations of the Riemann-Liouville(RL)fractional integral operator and several other fractional operators.Meanwhile,several generalizations are considered in order to demonstrate the novel variants involving a family of positive functions n(n∈N)for the proposed fractional operator.In order to confirm and demonstrate the proficiency of the characterized strategy,we analyze existing fractional integral operators in terms of classical fractional order.Meanwhile,some special cases are apprehended and the new outcomes are also illustrated.The obtained consequences illuminate that future research is easy to implement,profoundly efficient,viable,and exceptionally precise in its investigation of the behavior of non-linear differential equations of fractional order that emerge in the associated areas of science and engineering.
文摘In the present work, a unification of certain functions of mathematical physics is proposed and its properties are studied. The proposed function unifies Lommel function, Struve function, the Bessel-Maitland function and its generalization, Dotsenko function, generalized Mittag-Leffler function etc. The properties include absolute and uniform convergence, differential recurrence relation, integral representations in the form of Euler-Beta transform, Mellin-Barnes transform, Laplace transform and Whittaker transform. The special cases namely the generalized hypergeometric function, generalized Laguerre polynomial, Fox H-function etc. are also obtained.
文摘The principal aim of the paper is devoted to the study of some special properties of the Eα,βγ,q(Z) function for α =1/n . Authors defined the decomposition of the function Eα,βγ,q(Z) in the form of truncated power series as Equations (1.7), (1.8) and their various properties including Integral representation, Derivative, Inequalities and their several special cases are obtained. Some new results are also established for the function Eα,βγ,q(Z).
文摘In this paper, we use the Mittag-Leffler addition formula to solve the Green function of generalized time fractional diffusion equation in the whole plane and prove the convergence of the Green function.
基金Supported by the Scientific Research Fund of Jiangxi Provincial Department of Education(Grant No.GJJ191157)the Science and Technology support project of Pingxiang City(Grant No.2020C0102)the National Natural Science Foundation of China(Grant No.62063029).
文摘In the paper,by making use of the principle of subordination between analytic functions with the multiplier transforms defined by generalized Mittag-Leffler function,the authors investigate subclasses of univalent analytic functions,such as starlike functions,convex functions,close-to-convex functions and quasiconvex functions.Several inclusion relationships,inequality properties,subordination and superordination results associated with the multiplier transforms are proved and the sandwich-type results are also obtained.
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.
文摘Wind turbines are continuously exposed to harsh environmental and operational conditions throughout their lifetime,leading to the gradual degradation of their components.If left unaddressed,these degraded components can adversely affect turbine performance and significantly increase the likelihood of failure.As degradation progresses,the risk of failure escalates,making it essential to implement appropriate risk control measures.One effective risk control method involves performing inspection and monitoring activities that provide valuable insights into the condition of the structure,enabling the formulation of appropriate maintenance strategies based on accurate assessments.Supervisory Control and Data Acquisition(SCADA)systems offer low-resolution condition monitoring data that can be used for fault detection,diagnosis,quantification,prognosis,and maintenance planning.One commonly used method involves predicting power generation using SCADA data and comparing it against measured power generation.Significant discrepancies between predicted and measured values can indicate suboptimal operation,natural aging,or unnatural faults.Various predictive models,including parametric and non-parametric(statistical)approaches,have been proposed for estimating power generation.However,the imperfect nature of these models introduces uncertainties in the predicted power output.Additionally,SCADA monitoring data is prone to uncertainties arising from various sources.The presence of uncertainties from these two sources-imperfect predictive models and imperfect SCADA data-introduces uncertainty in the predicted power generation.This uncertainty complicates the process of determining whether discrepancies between measured and predicted values are significant enough to warrant maintenance actions.Depending on the nature of uncertainty-aleatory,arising from inherent randomness,or epistemic,stemming from incomplete knowledge or limited data-different analytical approaches,like Probabilistic and Possibilistic,can be applied for effective management.Both,Probabilistic and Possibilistic,Approaches offer distinct advantages and limitations.The Possibilistic Approach,rooted in fuzzy set theory,is particularly well suited for addressing epistemic uncertainties,especially those caused by imprecision or sparse statistical information.This makes it especially relevant for applications such as wind turbines,where it is often challenging to construct accurate probability distribution functions for environmental parameters due to limited sensor data from hard-to-access locations.This research focuses on developing a methodology for identifying suboptimal operation in wind turbines by comparing Grid Produced Power(Measured Produced Power)with Predicted Produced Power.To achieve this,the paper introduces a Possibilistic Approach for power prediction that accounts for uncertainties stemming from both model imperfections and measurement errors in SCADA data.The methodology combines machine learning models,used to establish predictive relationships between environmental inputs and power output,with a Possibilistic Framework that represents uncertainty through possibility distribution functions based on fuzzy logic and interval analysis.A real-world case study using operational SCADA data demonstrates the approach,with XGBoost selected as the final predictive model due to its strong accuracy and computational efficiency.
文摘A Langevin delayed fractional system with multiple delays in control,is a delayed fractional system that includes delay parameters in both state and control,is first introduced.This paper is devoted to investigating the relative controllability of the Langevin delayed fractional system with multiple delays in control.For linear systems to be relatively controllable,necessary and sufficient circumstances are identified by introducing and employing the Gramian matrix.The sufficient conditions for the relative controllability of semilinear systems are ofered based on Schauder's fixed point theorem.As an unusual approach,the controllability results of the delayed system are built for the first time on the exact solution produced by the MittagLeffler type function although controllability ones in the literature are built on the Volterra integral equations or the mild solutions produced by resolvent families.
基金Project supported by the National Key R&D Program of China(No.2021YFF0501001)the National Natural Science Foundation of China(Nos.52308315,51922046,and 52192661)+3 种基金the Research Funds of Huazhong University of Science and Technology(No.2023JCYJ014)the China Postdoctoral Science Foundation(No.2023M731206)the Research Funds of China Railway Siyuan Survey and Design Group Co.Ltd.(Nos.KY2023014S,KY2023126S,2021K085,2020K006,and 2020K172)the Autonomous Innovation Fund of Hubei Province of China(No.5003242027)。
文摘Optimizing wind energy harvesting performance remains a significant challenge.Machine learning(ML)offers a promising approach for addressing this challenge.This study proposes an ML-based approach using the radial basis function neural network(RBFNN)and differential evolution(DE)to predict and optimize the structural parameters(the diameter of the spherical bluff body D,the total spring stiffness k,and the length of the piezoelectric cantilever beam L)of the wind energy harvester(WEH).The RBFNN model is trained with theoretical data and validated with wind tunnel experimental results,achieving the coefficient-of-determination scores R2of 97.8%and 90.3%for predicting the average output power Pavgand aero-electro-mechanical efficiencyηaem,respectively.The DE algorithm is used to identify the optimal parameter combinations for wind speeds U ranging from 2.5 m/s to 6.5 m/s.The maximum Pavgis achieved when D=57.5 mm,k=28.8 N/m,L=112.1 mm,and U=4.6 m/s,while the maximumηaemis achieved when D=52.7 mm,k=29.2 N/m,L=89.2 mm,and U=4.7 m/s.Compared with that of the non-optimized structure,the WEH performance is improved by 28.6%in P_(avg)and 19.1%inη_(aem).
