Browsing by Author "Srivastava, H. M."

Now showing 1 - 20 of 26

Citation - WoS: 72
Citation - Scopus: 99
A Chebyshev spectral method based on operational matrix for fractional differential equations involving non-singular Mittag-Leffler kernel
(Springer, 2018) Baleanu, D.; Baleanu, Dumitru; Shiri, B.; Srivastava, H. M.; Al Qurashi, M.; 56389; Matematik
In this paper, we solve a system of fractional differential equations within a fractional derivative involving the Mittag-Leffler kernel by using the spectral methods. We apply the Chebyshev polynomials as a base and obtain the necessary operational matrix of fractional integral using the Clenshaw-Curtis formula. By applying the operational matrix, we obtain a system of linear algebraic equations. The approximate solution is computed by solving this system. The regularity of the solution investigated and a convergence analysis is provided. Numerical examples are provided to show the effectiveness and efficiency of the method.
Citation - WoS: 24
Citation - Scopus: 27
A New Neumann Series Method for Solving A Family of Local Fractional Fredholm and Volterra Integral Equations
(Hindawi Ltd, 2013) Ma, Xiao-Jing; Baleanu, Dumitru; Srivastava, H. M.; Baleanu, Dumitru; Yang, Xiao-Jun; 56389; Matematik
We propose a new Neumann series method to solve a family of local fractional Fredholm and Volterra integral equations. The integral operator, which is used in our investigation, is of the local fractional integral operator type. Two illustrative examples show the accuracy and the reliability of the obtained results.
Citation - WoS: 0
Citation - Scopus: 9
Advanced Topics in Fractional Dynamics
(Hindawi Ltd, 2013) Baleanu, Dumitru; Baleanu, Dumitru; Srivastava, H. M.; Daftardar-Gejji, Varsha; Li, Changpin; Machado, J. A. Tenreiro; 56389; Matematik
Citation - WoS: 99
Citation - Scopus: 113
An efficient computational approach for a fractional-order biological population model with carrying capacity
(Pergamon-elsevier Science Ltd, 2020) Srivastava, H. M.; Baleanu, Dumitru; Dubey, V. P.; Kumar, R.; Singh, J.; Kumar, D.; Baleanu, D.; 56389; Matematik
In this article, we examine a fractional-order biological population model with carrying capacity. The blended homotopy techniques pertaining to the Sumudu transform are utilized to explore the solutions of a nonlinear fractional-order population model with carrying capacity. The fractional derivative of the Caputo type is utilized in the proposed investigation. The numerical computations indicate the sufficiency of the iterations for the improved estimations of the solutions of this fractional-order biological population model which exemplifies the potency and soundness of the utilized schemes. The analysis explored through the utilization of the projected methods reveals that both of the schemes are in a great agreement with each other. The variations of the prey and predator populations with respect to time and fractional order of the Caputo derivative are presented and graphically illustrated. (c) 2020 Elsevier Ltd. All rights reserved.
Citation - WoS: 146
Citation - Scopus: 152
Cantor-Type Cylindrical-Coordinate Method For Differential Equations With Local Fractional Derivatives
(Elsevier Science Bv, 2013) Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, H. M.; He, Ji-Huan; Baleanu, Dumitru; 56389; Matematik
In this Letter, we propose to use the Cantor-type cylindrical-coordinate method in order to investigate a family of local fractional differential operators on Cantor sets. Some testing examples are given to illustrate the capability of the proposed method for the heat-conduction equation on a Cantor set and the damped wave equation in fractal strings. It is seen to be a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type cylindrical-coordinate systems. (c) 2013 Published by Elsevier B.V.
Citation - WoS: 0
Coordinate systems of Cantor-type cylindrical and Cantor-type spherical coordinates
(Academic Press Ltd-elsevier Science Ltd, 2016) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; Srivastava, H. M.; 56389; Matematik
Corrigendum to Series Representations for Fractional-Calculus Operators Involving Generalised Mittag-Leffler Functions
(Elsevier B.V., 2020) Baleanu, Dumitru; Baleanu, Dumitru; Srivastava, H. M.; 56389; Matematik
This corrigendum corrects two equations presented in the paper “Series representations for fractional-calculus operators involving generalised Mittag-Leffler functions” [Commun. Nonlinear Sci. Numer. Simulat. 67 (2019) 517–527]. One error is inconsequential, while the other leads to a missing factor in the statement of one theorem.
Citation - WoS: 0
Coupling the local fractional Laplace transform with analytic methods
(Academic Press Ltd-elsevier Science Ltd, 2016) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; Srivastava, H. M.; 56389; Matematik
Citation - WoS: 4
Introduction to local fractional derivative and integral operators
(Academic Press Ltd-elsevier Science Ltd, 2016) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; Srivastava, H. M.; 56389; Matematik
Citation - WoS: 0
Local fractional derivatives of elementary functions
(Academic Press Ltd-elsevier Science Ltd, 2016) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; Srivastava, H. M.; 56389; Matematik
Citation - WoS: 1
Local fractional Fourier series
(Academic Press Ltd-elsevier Science Ltd, 2016) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; Srivastava, H. M.; 56389; Matematik
Citation - WoS: 0
Local fractional Fourier transform and applications
(Academic Press Ltd-elsevier Science Ltd, 2016) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; Srivastava, H. M.; 56389; Matematik
Citation - WoS: 0
Local Fractional Integral Transforms and Their Applications Preface
(Academic Press Ltd-elsevier Science Ltd, 2016) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; Srivastava, H. M.; 56389; Matematik
Citation - WoS: 7
Local fractional Laplace transform and applications
(Academic Press Ltd-elsevier Science Ltd, 2016) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; Srivastava, H. M.; 56389; Matematik
Citation - WoS: 0
Local fractional Maclaurin's series of elementary functions
(Academic Press Ltd-elsevier Science Ltd, 2016) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; Srivastava, H. M.; 56389; Matematik
Citation - WoS: 146
Citation - Scopus: 143
Local fractional similarity solution for the diffusion equation defined on Cantor sets
(Pergamon-elsevier Science Ltd, 2015) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; Srivastava, H. M.; Matematik
In this letter, the local fractional similarity solution is addressed for the non-differentiable diffusion equation. Structuring the similarity transformations via the rule of the local fractional partial derivative operators, we transform the diffusive operator into a similarity ordinary differential equation. The obtained result shows the non-differentiability of the solution suitable to describe the properties and behaviors of the fractal content. (C) 2015 Published by Elsevier Ltd.
Citation - WoS: 41
Citation - Scopus: 77
Local Fractional Sumudu Transform with Application to IVPs on Cantor Sets
(Hindawi Ltd, 2014) Srivastava, H. M.; Baleanu, Dumitru; Golmankhaneh, Alireza Khalili; Baleanu, Dumitru; Yang, Xiao-Jun; 56389; Matematik
Local fractional derivatives were investigated intensively during the last few years. The coupling method of Sumudu transform and local fractional calculus (called as the local fractional Sumudu transform) was suggested in this paper. The presented method is applied to find the non differentiable analytical solutions for initial value problems with local fractional derivative. The obtained results are given to show the advantages.
Citation - WoS: 26
Citation - Scopus: 22
On Local Fractional Continuous Wavelet Transform
(Hindawi Ltd, 2013) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; Srivastava, H. M.; Tenreiro Machado, J. A.; 56389; Matematik
We introduce a new wavelet transform within the framework of the local fractional calculus. An illustrative example of local fractional wavelet transform is also presented.
Citation - WoS: 4
Citation - Scopus: 4
Preface: Recent Advances in Fractional Dynamics
(Amer inst Physics, 2016) Srivastava, H. M.; Baleanu, Dumitru; Baleanu, Dumitru; Li, Changpin; 56389; Matematik
This Special Focus Issue contains several recent developments and advances on the subject of Fractional Dynamics and its widespread applications in various areas of the mathematical, physical, and engineering sciences. Published by AIP Publishing.
Citation - WoS: 121
Citation - Scopus: 128
Series representations for fractional-calculus operators involving generalised Mittag-Leffler functions
(Elsevier, 2019) Fernandez, Arran; Baleanu, Dumitru; Baleanu, Dumitru; Srivastava, H. M.; 56389; Matematik
We consider an integral transform introduced by Prabhakar, involving generalised multi-parameter Mittag-Leffler functions, which can be used to introduce and investigate several different models of fractional calculus. We derive a new series expression for this transform, in terms of classical Riemann-Liouville fractional integrals, and use it to obtain or verify series formulae in various specific cases corresponding to different fractional-calculus models. We demonstrate the power of our result by applying the series formula to derive analogues of the product and chain rules in more general fractional contexts. We also discuss how the Prabhakar model can be used to explore the idea of fractional iteration in connection with semigroup properties. (C) 2018 Elsevier B.V. All rights reserved.