Browsing by Author "Srivastava, H. M."
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Editorial Citation - Scopus: 9Advanced Topics in Fractional Dynamics(Hindawi Ltd, 2013) Srivastava, H. M.; Daftardar-Gejji, Varsha; Li, Changpin; Machado, J. A. Tenreiro; Baleanu, Dumitru; Tenreiro Machado, J.A.Book Part The Analogues of Trigonometric Functions Defined on Cantor Sets(Academic Press Ltd-elsevier Science Ltd, 2016) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; Srivastava, H. M.; MatematikArticle Citation - WoS: 148Citation - Scopus: 155Cantor-Type Cylindrical-Coordinate Method for Differential Equations With Local Fractional Derivatives(Elsevier Science Bv, 2013) Srivastava, H. M.; He, Ji-Huan; Baleanu, Dumitru; Yang, Xiao-JunIn 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.Article Citation - WoS: 77Citation - Scopus: 104A Chebyshev Spectral Method Based on Operational Matrix for Fractional Differential Equations Involving Non-Singular Mittag-Leffler Kernel(Springer, 2018) Shiri, B.; Srivastava, H. M.; Al Qurashi, M.; Baleanu, D.; Al Qurashi, M.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.Book Part 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.; MatematikArticle Corrigendum to Series Representations for Fractional-Calculus Operators Involving Generalised Mittag-Leffler Functions(Elsevier B.V., 2020) Fernandez, Arran; Baleanu, Dumitru; Srivastava, H. M.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.Book Part Coupling the Local Fractional Laplace Transform With Analytic Methods(Academic Press Ltd-elsevier Science Ltd, 2016) Baleanu, Dumitru; Srivastava, H. M.; Yang, Xiao-JunArticle Citation - WoS: 101Citation - Scopus: 116An Efficient Computational Approach for a Fractional-Order Biological Population Model With Carrying Capacity(Pergamon-elsevier Science Ltd, 2020) Dubey, V. P.; Kumar, R.; Singh, J.; Kumar, D.; Baleanu, D.; Srivastava, H. M.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.Editorial Citation - WoS: 4Introduction To Local Fractional Derivative and Integral Operators(Academic Press Ltd-elsevier Science Ltd, 2016) Baleanu, Dumitru; Srivastava, H. M.; Yang, Xiao-JunBook Part Local Fractional Derivatives of Elementary Functions(Academic Press Ltd-elsevier Science Ltd, 2016) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; Srivastava, H. M.; MatematikBook Part Citation - WoS: 1Local Fractional Fourier Series(Academic Press Ltd-elsevier Science Ltd, 2016) Baleanu, Dumitru; Srivastava, H. M.; Yang, Xiao-JunBook Part Local Fractional Fourier Transform and Applications(Academic Press Ltd-elsevier Science Ltd, 2016) Baleanu, Dumitru; Srivastava, H. M.; Yang, Xiao-JunEditorial 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.; MatematikBook Part Citation - WoS: 7Local Fractional Laplace Transform and Applications(Academic Press Ltd-elsevier Science Ltd, 2016) Baleanu, Dumitru; Srivastava, H. M.; Yang, Xiao-JunBook Part 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.; MatematikArticle Citation - WoS: 148Citation - Scopus: 144Local Fractional Similarity Solution for the Diffusion Equation Defined on Cantor Sets(Pergamon-elsevier Science Ltd, 2015) Baleanu, Dumitru; Srivastava, H. M.; Yang, Xiao-JunIn 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.Article Citation - WoS: 43Citation - Scopus: 80Local Fractional Sumudu Transform With Application To Ivps on Cantor Sets(Hindawi Ltd, 2014) Golmankhaneh, Alireza Khalili; Baleanu, Dumitru; Yang, Xiao-Jun; Srivastava, H. M.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.Article Citation - WoS: 24Citation - Scopus: 27A New Neumann Series Method for Solving a Family of Local Fractional Fredholm and Volterra Integral Equations(Hindawi Ltd, 2013) Srivastava, H. M.; Baleanu, Dumitru; Yang, Xiao-Jun; Ma, Xiao-JingWe 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.Article Citation - WoS: 26Citation - Scopus: 22On Local Fractional Continuous Wavelet Transform(Hindawi Ltd, 2013) Tenreiro Machado, J. A.; Baleanu, Dumitru; Srivastava, H. M.; Yang, Xiao-JunWe introduce a new wavelet transform within the framework of the local fractional calculus. An illustrative example of local fractional wavelet transform is also presented.Editorial Citation - WoS: 4Citation - Scopus: 4Preface: Recent Advances in Fractional Dynamics(Amer inst Physics, 2016) Baleanu, Dumitru; Li, Changpin; Srivastava, H. M.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.
