As a result of the authors＇ error, the paper ＂Determination of the chromospheric quiet network element area index and its variation between 2008 and 2011＂ by Singh, J. et al. （RAA, Vol. 12, p.201 [2012]） contains...As a result of the authors＇ error, the paper ＂Determination of the chromospheric quiet network element area index and its variation between 2008 and 2011＂ by Singh, J. et al. （RAA, Vol. 12, p.201 [2012]） contains errors in page 206. In the original article, the top right and bottom images were inadvertently interchanged in Figure 5. The correct sequence of images is shown in this erratum. Figure caption and details about the images remain unchanged.展开更多
In this paper,the local fractional natural decomposition method(LFNDM)is used for solving a local fractional Poisson equation.The local fractional Poisson equation plays a significant role in the study of a potential ...In this paper,the local fractional natural decomposition method(LFNDM)is used for solving a local fractional Poisson equation.The local fractional Poisson equation plays a significant role in the study of a potential field due to a fixed electric charge or mass density distribution.Numerical examples with computer simulations are presented in this paper.The obtained results show that LFNDM is effective and convenient for application.展开更多
A combined uniform and long-time series of Ca-K images from the Kodaikanal Observatory,Mount Wilson Observatory and Mauna Loa Solar Observatory was used to identify and study the Ca-K small-scale features and their so...A combined uniform and long-time series of Ca-K images from the Kodaikanal Observatory,Mount Wilson Observatory and Mauna Loa Solar Observatory was used to identify and study the Ca-K small-scale features and their solar cycle variations over a century.The small scale features are classified into three distinct categories:enhanced network,active network and quiet network.All these features show that their areas vary according to the11 yr solar cycle.The relative amplitude of the Ca-K network variations agrees with that of the sunspot cycle.The total area of these small-scale features varies from about 5%during the minimum phase of the solar cycle to about20%during its maximum phase.展开更多
The Ca II K filtergrams from Kodaikanal Solar Observatory have been used to study solar activity. The images are dominated by the chromospheric network and plages. Programs have been developed to obtain the network an...The Ca II K filtergrams from Kodaikanal Solar Observatory have been used to study solar activity. The images are dominated by the chromospheric network and plages. Programs have been developed to obtain the network and plage indices from the daily images as functions of solar latitude and time. Preliminary results from the analysis are reported here. The network and plage indices were found to follow the sunspot cycle. A secondary peak is found during the period of declining activity in both the indices. A comparison of network indices from the northern and the southern hemispheres shows that the former is more active than the latter. However such an asymmetry is not clearly seen in the plage index.展开更多
In general, it is believed that plages and sunspots are the main contribu- tors to solar irradiance. There are small-scale structures on the Sun with intermediate magnetic fields that could also contribute to solar ir...In general, it is believed that plages and sunspots are the main contribu- tors to solar irradiance. There are small-scale structures on the Sun with intermediate magnetic fields that could also contribute to solar irradiance, but it has not yet been quantified how many of these small scale structures contribute and how much this varies over the solar cycle. We used Ca II K images obtained from the telescope at the Kodaikanal observatory. We report a method to separate the network elements from the background structure and plage regions, and compute the changes in the network element area index during the minimum phase of the solar cycle and part of the as- cending phase of cycle 24. The measured area occupied by the network elements is about 30% and the plages cover less than 1% of the solar disk during the observation period from February 2008 to 2011. During the extended period of minimum activity, it is observed that the network element area index decreases by about 7% compared to the area occupied by the network elements in 2008. A long term study of the network element area index is required to understand the variations over the solar cycle.展开更多
In this paper,we analyze the dynamical behavior of fish farm model related to Atangana-Baleanu derivative of arbitrary order.The rnodel is constituted with the group of non-linear differential equations having nutrien...In this paper,we analyze the dynamical behavior of fish farm model related to Atangana-Baleanu derivative of arbitrary order.The rnodel is constituted with the group of non-linear differential equations having nutrients,fish and mussel.We have included discrete kind gestational delay of fish.The solution of fish farm model is determined by employing homotopy analysis transforms method(HATM).Existence of and uniqueness of solution are studied through Picard-Lindelof approach.The influence of order of new non-integer order derivative on nutrients,fish and mussel is discussed.The complete study reveals that the outer food supplies manage the behavior of the model.Moreover,to show the outcomes of the study,some numerical results are demonstrated through graphs.展开更多
This article is devoted to a newly introduced numerical method for time-fractional dispersive partial differential equation in a multidimensional space.The time-fractional dispersive partial differential equation play...This article is devoted to a newly introduced numerical method for time-fractional dispersive partial differential equation in a multidimensional space.The time-fractional dispersive partial differential equation plays a great role in solving the problems arising in ocean science and engineering.The numerical technique comprises of Sumudu transform,homotopy perturbation scheme and He’s polynomial,namely homotopy perturbation Sumudu transform method(HPSTM)is efficiently used to examine time-fractional dispersive partial differential equation of third order in multi-dimensional space.The approximate analytic solution of the time-fractional dispersive partial differential equation of third-order in multi-dimensional space obtained by HPSTM is compared with exact solution as well as the solution obtained by using Adomain decomposition method.The results derived with the aid of two techniques are in a good agreement and consequently these techniques may be considered as an alternative and efficient approach for solving fractional partial differential equations.Several test problems are experimented to confirm the accuracy and efficiency of the proposed methods.展开更多
In this paper,an efficient hybrid numerical scheme which is based on a joint venture of the q-homotopy analysis method and Sumudu transform is applied to investigate the time-fractional modified Degasperis-Procesi(DP)...In this paper,an efficient hybrid numerical scheme which is based on a joint venture of the q-homotopy analysis method and Sumudu transform is applied to investigate the time-fractional modified Degasperis-Procesi(DP)equation.The present study considers the Caputo fractional derivative.The fractional order modified DP model is very important and plays a great role in study of ocean engineering and science.The proposed scheme provides a beautiful opportunity for proper selection of the auxiliary parameter h and the asymptotic parameterρ(≥1)to handle mainly the differential equations of nonlinear nature.The offered scheme produces the solution in the shape of a convergent series in a large admissible domain which is helpful to regulate the region of convergence of a series solution.The proposed work computes the approximate analytical solution of the fractional modified DP equation systematically and also presents graphically the variation of the obtained solution for diverse values of the fractional parameterβ.展开更多
In this work,we apply an efficient analytical algorithm namely homotopy perturbation Sumudu transform method(HPSTM)to find the exact and approximate solutions of linear and nonlinear time-fractional regularized long w...In this work,we apply an efficient analytical algorithm namely homotopy perturbation Sumudu transform method(HPSTM)to find the exact and approximate solutions of linear and nonlinear time-fractional regularized long wave(RLW)equations.The RLW equations describe the nature of ion acoustic waves in plasma and shallow water waves in oceans.The derived results are very significant and imperative for explaining various physical phenomenons.The suggested method basically demonstrates how two efficient techniques,the Sumudu transform scheme and the homotopy perturbation technique can be integrated and applied to find exact and approximate solutions of linear and nonlinear time-fractional RLW equations.The nonlinear expressions can be simply managed by application of He’s polynomials.The result shows that the HPSTM is very powerful,efficient,and simple and it eliminates the round-off errors.It has been observed that the proposed technique can be widely employed to examine other real world problems.展开更多
文摘As a result of the authors＇ error, the paper ＂Determination of the chromospheric quiet network element area index and its variation between 2008 and 2011＂ by Singh, J. et al. （RAA, Vol. 12, p.201 [2012]） contains errors in page 206. In the original article, the top right and bottom images were inadvertently interchanged in Figure 5. The correct sequence of images is shown in this erratum. Figure caption and details about the images remain unchanged.
文摘In this paper,the local fractional natural decomposition method(LFNDM)is used for solving a local fractional Poisson equation.The local fractional Poisson equation plays a significant role in the study of a potential field due to a fixed electric charge or mass density distribution.Numerical examples with computer simulations are presented in this paper.The obtained results show that LFNDM is effective and convenient for application.
基金supported by the International Space Science Institute (ISSI),Bern,Switzerland and ISSI-Beijing,China。
文摘A combined uniform and long-time series of Ca-K images from the Kodaikanal Observatory,Mount Wilson Observatory and Mauna Loa Solar Observatory was used to identify and study the Ca-K small-scale features and their solar cycle variations over a century.The small scale features are classified into three distinct categories:enhanced network,active network and quiet network.All these features show that their areas vary according to the11 yr solar cycle.The relative amplitude of the Ca-K network variations agrees with that of the sunspot cycle.The total area of these small-scale features varies from about 5%during the minimum phase of the solar cycle to about20%during its maximum phase.
基金funded by the Department of Science and Technology,Government of India
文摘The Ca II K filtergrams from Kodaikanal Solar Observatory have been used to study solar activity. The images are dominated by the chromospheric network and plages. Programs have been developed to obtain the network and plage indices from the daily images as functions of solar latitude and time. Preliminary results from the analysis are reported here. The network and plage indices were found to follow the sunspot cycle. A secondary peak is found during the period of declining activity in both the indices. A comparison of network indices from the northern and the southern hemispheres shows that the former is more active than the latter. However such an asymmetry is not clearly seen in the plage index.
文摘In general, it is believed that plages and sunspots are the main contribu- tors to solar irradiance. There are small-scale structures on the Sun with intermediate magnetic fields that could also contribute to solar irradiance, but it has not yet been quantified how many of these small scale structures contribute and how much this varies over the solar cycle. We used Ca II K images obtained from the telescope at the Kodaikanal observatory. We report a method to separate the network elements from the background structure and plage regions, and compute the changes in the network element area index during the minimum phase of the solar cycle and part of the as- cending phase of cycle 24. The measured area occupied by the network elements is about 30% and the plages cover less than 1% of the solar disk during the observation period from February 2008 to 2011. During the extended period of minimum activity, it is observed that the network element area index decreases by about 7% compared to the area occupied by the network elements in 2008. A long term study of the network element area index is required to understand the variations over the solar cycle.
文摘In this paper,we analyze the dynamical behavior of fish farm model related to Atangana-Baleanu derivative of arbitrary order.The rnodel is constituted with the group of non-linear differential equations having nutrients,fish and mussel.We have included discrete kind gestational delay of fish.The solution of fish farm model is determined by employing homotopy analysis transforms method(HATM).Existence of and uniqueness of solution are studied through Picard-Lindelof approach.The influence of order of new non-integer order derivative on nutrients,fish and mussel is discussed.The complete study reveals that the outer food supplies manage the behavior of the model.Moreover,to show the outcomes of the study,some numerical results are demonstrated through graphs.
文摘This article is devoted to a newly introduced numerical method for time-fractional dispersive partial differential equation in a multidimensional space.The time-fractional dispersive partial differential equation plays a great role in solving the problems arising in ocean science and engineering.The numerical technique comprises of Sumudu transform,homotopy perturbation scheme and He’s polynomial,namely homotopy perturbation Sumudu transform method(HPSTM)is efficiently used to examine time-fractional dispersive partial differential equation of third order in multi-dimensional space.The approximate analytic solution of the time-fractional dispersive partial differential equation of third-order in multi-dimensional space obtained by HPSTM is compared with exact solution as well as the solution obtained by using Adomain decomposition method.The results derived with the aid of two techniques are in a good agreement and consequently these techniques may be considered as an alternative and efficient approach for solving fractional partial differential equations.Several test problems are experimented to confirm the accuracy and efficiency of the proposed methods.
文摘In this paper,an efficient hybrid numerical scheme which is based on a joint venture of the q-homotopy analysis method and Sumudu transform is applied to investigate the time-fractional modified Degasperis-Procesi(DP)equation.The present study considers the Caputo fractional derivative.The fractional order modified DP model is very important and plays a great role in study of ocean engineering and science.The proposed scheme provides a beautiful opportunity for proper selection of the auxiliary parameter h and the asymptotic parameterρ(≥1)to handle mainly the differential equations of nonlinear nature.The offered scheme produces the solution in the shape of a convergent series in a large admissible domain which is helpful to regulate the region of convergence of a series solution.The proposed work computes the approximate analytical solution of the fractional modified DP equation systematically and also presents graphically the variation of the obtained solution for diverse values of the fractional parameterβ.
文摘In this work,we apply an efficient analytical algorithm namely homotopy perturbation Sumudu transform method(HPSTM)to find the exact and approximate solutions of linear and nonlinear time-fractional regularized long wave(RLW)equations.The RLW equations describe the nature of ion acoustic waves in plasma and shallow water waves in oceans.The derived results are very significant and imperative for explaining various physical phenomenons.The suggested method basically demonstrates how two efficient techniques,the Sumudu transform scheme and the homotopy perturbation technique can be integrated and applied to find exact and approximate solutions of linear and nonlinear time-fractional RLW equations.The nonlinear expressions can be simply managed by application of He’s polynomials.The result shows that the HPSTM is very powerful,efficient,and simple and it eliminates the round-off errors.It has been observed that the proposed technique can be widely employed to examine other real world problems.
