Browsing by Author "Srivastava, H. M."

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Citation Count: Baleanu, D...et al. (2018). A Chebyshev spectral method based on operational matrix for fractional differential equations involving non-singular Mittag-Leffler kernel, Advances in Difference Equations.
A Chebyshev spectral method based on operational matrix for fractional differential equations involving non-singular Mittag-Leffler kernel
(Pushpa Publishing House, 2018) Baleanu, Dumitru; Shiri, B.; Srivastava, H. M.; Al Qurashi, Maysaa Mohamed; 56389
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 Count: Ma, Xiao-Jing...et al. (2018). "A New Neumann Series Method for Solving a Family of Local Fractional Fredholm and Volterra Integral Equations", Mathematical Problems In Engineering, (2018)
A New Neumann Series Method for Solving A Family of Local Fractional Fredholm and Volterra Integral Equations
(Hindawi LTD, 2013) Ma, Xiao-Jing; Srivastava, H. M.; Baleanu, Dumitru; Yang, Xiao-Jun; 56389
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 Count: Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, H. M. (2021). "Advanced Analysis of Local Fractional Calculus Applied to the Rice Theory in Fractal Fracture Mechanics", in Methods of Mathematical Modelling and Computation for Complex Systems, Vol. 373, pp. 105-133.
Advanced Analysis of Local Fractional Calculus Applied to the Rice Theory in Fractal Fracture Mechanics
(2021) Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, H. M.; 56389
In this chapter, the recent results for the analysis of local fractional calculus are considered for the first time. The local fractional derivative (LFD) and the local fractional integral (LFI) in the fractional (real and complex) sets, the series and transforms involving the Mittag-Leffler function defined on Cantor sets are introduced and reviewed. The uniqueness of the solutions of the local fractional differential and integral equations and the local fractional inequalities are considered in detail. The local fractional vector calculus is applied to describe the Rice theory in fractal fracture mechanics.
Citation Count: Baleanu, Dumitru...et al. (2013). "Advanced Topics in Fractional Dynamics", Advances in Mathematical Physics.
Advanced Topics in Fractional Dynamics
(Hindawi LTD, 2013) Baleanu, Dumitru; Srivastava, H. M.; Daftardar-Gejji, Varsha; Li, Changpin; Machado, J. A. Tenreiro; 56389
Citation Count: Srivastava, H.M...et al. (2015). "Advances On Integrodifferential Equations and Transforms", Abstract and Applied Analysis, Vol. 2015.
Advances On Integrodifferential Equations and Transforms
(Hindawi Publishing Corporation, 2015) Srivastava, H. M.; Yang, Xiao-Jun; Baleanu, Dumitru; Nieto, Juan J.; Hristov, Jordan,; 56389
Citation Count: Srivastava, H. M...et al. (2020). "An efficient computational approach for a fractional-order biological population model with carrying capacity", Chaos Solitons & Fractals, Vol. 138.
An efficient computational approach for a fractional-order biological population model with carrying capacity
(2020) Srivastava, H. M.; Dubey, V. P.; Kumar, R.; Singh, J.; Kumar, D.; Baleanu, Dumitru; 56389
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.
Cantor-Type Cylindrical-Coordinate Method For Differential Equations With Local Fractional Derivatives
(Elsevier Science, 2013) Yang, Xiao-Jun; Srivastava, H. M.; Baleanu, Dumitru; He, Ji-Huan; 56389
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 Count: Fernandez, A.; Baleanu, D.; Srivastava, H.M., " Corrigendum to Series Representations for Fractional-Calculus Operators Involving Generalised Mittag-Leffler Functions", Communications in Nonlinear Science and Numerical Simulation, Vol. 82, (2020).
Corrigendum to Series Representations for Fractional-Calculus Operators Involving Generalised Mittag-Leffler Functions
(Elsevier B.V., 2020) Fernandez, Arran; Baleanu, Dumitru; Srivastava, H. M.; 56389
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 Count: Pinto, Carla M. A...et al. (2019). "Efficacy of the Post-Exposure Prophylaxis and of the HIV Latent Reservoir in HIV Infection", Mathematics, Vol. 7, No. 6.
Efficacy of the Post-Exposure Prophylaxis and of the HIV Latent Reservoir in HIV Infection
(MDPI, 2019) Pinto, Carla M. A.; Carvalho, Ana R. M.; Baleanu, Dumitru; Srivastava, H. M.; 56389
We propose a fractional order model to study the efficacy of the Post-Exposure Prophylaxis (PEP) in human immunodeficiency virus (HIV) within-host dynamics, in the presence of the HIV latent reservoir. Latent reservoirs harbor infected cells that contain a transcriptionally silent but reactivatable provirus. The latter constitutes a major difficulty to the eradication of HIV in infected patients. PEP is used as a way to prevent HIV infection after a recent possible exposure to HIV. It consists of the in-take of antiretroviral drugs for, usually, 28 days. In this study, we focus on the dosage and dosage intervals of antiretroviral therapy (ART) during PEP and in the role of the latent reservoir in HIV infected patients. We thus simulate the model for immunologically important parameters concerning the drugs and the fraction of latently infected cells. The results may add important information to clinical practice of HIV infected patients.
Citation Count: Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, H. M. (2016). "Local fractional derivatives of elementary functions", LOCAL FRACTIONAL INTEGRAL TRANSFORMS AND THEIR APPLICATIONS, pp. 207-209.
Local fractional derivatives of elementary functions
(2016) Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, H. M.; 56389
Citation Count: Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, H. M., "Local fractional Fourier series", Local Fractional Integral Transforms and Their Applications, pp. 57-94, (2016).
Local fractional Fourier series
(Elsevier Science LTD, 2016) Baleanu, Dumitru; Yang, Xiao-Jun; Srivastava, H. M.; 56389
Citation Count: Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, H. M., "Local Fractional Integral Transforms and Their Applications Preface", Local Fractional Integral Transforms and Their Applications, pp. XI, (2016).
Local Fractional Integral Transforms and Their Applications Preface
(Elsevier Science LTD, 2016) Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, H. M.; 56389
Citation Count: Yang, X.J., Baleanu,D., Srivastava, H.M. (2015). Local fractional similarity solution for the diffusion equation defined on Cantor sets. Applied Mathematics Letters, 47, 54-60. http://dx.doi.org/10.1016/j.aml.2015.02.024
Local fractional similarity solution for the diffusion equation defined on Cantor sets
(Pergamon-Elsevier Science LTD, 2015) Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, H. M.
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.
Local Fractional Sumudu Transform with Application to IVPs on Cantor Sets
(Hindawi LTD, 2014) Srivastava, H. M.; Golmankhaneh, Alireza K.; Baleanu, Dumitru; Yang, Xiao-Jun; 56389
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.
On Local Fractional Continuous Wavelet Transform
(Hindawi LTD, 2013) Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, H. M.; Tenreiro Machado, J. A.; 56389
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 Count: Srivastava, H. M.; Baleanu, Dumitru; Li, Changpin, "Preface: Recent Advances in Fractional Dynamics", Chaos, Vol. 26, No. 8, (2016).
Preface: Recent Advances in Fractional Dynamics
(Amer Inst Physics, 2016) Srivastava, H. M.; Baleanu, Dumitru; Li, Changpin; 56389
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 Count: Fernandez, Arran; Baleanu, Dumitru; Srivastava, H. M., "Series representations for fractional-calculus operators involving generalised Mittag-Leffler functions", Communications in Nonlinear Science And Numerical Simulation, Vol. 67, pp. 517-527, (2019).
Series representations for fractional-calculus operators involving generalised Mittag-Leffler functions
(Elsevier Science BV, 2019) Fernandez, Arran; Baleanu, Dumitru; Srivastava, H. M.; 56389
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.
Citation Count: Singh, Harendra...et al. (2020). "Solution of multi-dimensional Fredholm equations using Legendre scaling functions", Applied Numerical Mathematics, Vol. 150, pp. 313-324.
Solution of multi-dimensional Fredholm equations using Legendre scaling functions
(2020) Singh, Harendra; Baleanu, Dumitru; Srivastava, H. M.; Dutta, Hemen; Jha, Navin Kumar; 56389
In this article, we construct approximate solution to multi-dimensional Fredholm integral equations of second kind using n-dimensional Legendre scaling functions. Error analysis of the problem is provided in the L-2 sense. It is shown that our numerical method is numerically stable. Some examples are discussed based on proposed method to show the importance and accuracy of the proposed numerical method. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.
Citation Count: Srivastava, Hari M.; Fernandez, Arran; Baleanu, Dumitru, "Some New Fractional-Calculus Connections between Mittag-Leffler Functions", Mathematics, Vol. 7, No. 6, (June 2019).
Some New Fractional-Calculus Connections between Mittag-Leffler Functions
(MDPI, 2019) Srivastava, H. M.; Fernandez, Arran; Baleanu, Dumitru; 56389
We consider the well-known Mittag-Leffler functions of one, two and three parameters, and establish some new connections between them using fractional calculus. In particular, we express the three-parameter Mittag-Leffler function as a fractional derivative of the two-parameter Mittag-Leffler function, which is in turn a fractional integral of the one-parameter Mittag-Leffler function. Hence, we derive an integral expression for the three-parameter one in terms of the one-parameter one. We discuss the importance and applications of all three Mittag-Leffler functions, with a view to potential applications of our results in making certain types of experimental data much easier to analyse.
Citation Count: Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, H. M. (2016). "Tables of local fractional Fourier transform operators", LOCAL FRACTIONAL INTEGRAL TRANSFORMS AND THEIR APPLICATIONS, pp. 223-223.
Tables of local fractional Fourier transform operators
(2016) Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, H. M.; 56389