The Modified Fractional Power Series Method for Solving Fractional Non-isothermal Reaction–Diffusion Model Equations in a Spherical Catalyst

Syam, Muhammed I.; Anwar, Mohamed-Naim Yehia; Yıldırım, Ahmet; Syam, Mahmmoud M.

doi:10.1007/s40819-019-0624-0

Cited by 12 publications

(1 citation statement)

References 14 publications

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“…It is significant to find new solutions of these equations for understanding the physical phenomenon. In recent years, various methods such as Kudryashov expansion and auxiliary equation method [3], modified fractional power series method [4], fractional Adams-Bashforth method [5], tanh-type and sech-type solitons [6], and Jacobi polynomials approach [7] have been implemented to find new exact and numerical solutions of the numerous types of FPDEs.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of fractional Dullin–Gottwald–Holm equation for solitary shallow water waves

Ray

Sagar

2022

Numerical Methods Partial

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In this paper, a numerical scheme to solve the time-fractional Dullin-Gottwald-Holm equation has been proposed. The proposed scheme is based on approximating the solution using multiquadric radial basis function. The fractional derivatives are described in the Caputo sense. The obtained numerical results are compared with exact solution to confirm the accuracy and effectiveness of the presented scheme.

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Section: Introductionmentioning

confidence: 99%

Numerical solution of fractional Dullin–Gottwald–Holm equation for solitary shallow water waves

Ray

Sagar

2022

Numerical Methods Partial

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An efficient numerical method for the distributed‐order time‐fractional diffusion equation with the error analysis and stability properties

Irandoust‐Pakchin,

Hossein Derakhshan,

Rezapour

et al. 2024

Math Methods in App Sciences

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In this manuscript, we study and examine the time‐fractional modified anomalous sub‐diffusion model of distributed‐order. Two numerical approaches are used to study the approximate solutions of the presented model. For the first approach, we use a second‐order difference method based on the L1 formula for the temporal variable. In this case, stability and convergence analysis for time discretization using the L1 formula is displayed. For the second approach, we display and demonstrate the numerical method for the full‐discrete based on the Galerkin weak form based on various kernels and shape functions of reproducing kernel particle method which do not have the ‐Kronecker property. Moreover, in this manuscript, in order to be able to use the necessary boundary conditions, the two straight strategies are used: one is the Lagrange multiplier method, and the other one is the penalty method. By using penalty method, we can the main boundary value model is changed to a new BVP with Robin boundary condition. At the end of the article, some numerical examples are presented and analyzed for the efficiency of the proposed numerical method. Also, the presented numerical method is compared with other numerical approaches, and the results of this comparison are reported in the form of a table.

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Numerical solution of fractional Kersten–Krasil’shchik coupled KdV–mKdV system arising in shallow water waves

Sagar

Ray²

2022

Comp. Appl. Math.

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The Modified Fractional Power Series Method for Solving Fractional Non-isothermal Reaction–Diffusion Model Equations in a Spherical Catalyst

Cited by 12 publications

References 14 publications

Numerical solution of fractional Dullin–Gottwald–Holm equation for solitary shallow water waves

Numerical solution of fractional Dullin–Gottwald–Holm equation for solitary shallow water waves

An efficient numerical method for the distributed‐order time‐fractional diffusion equation with the error analysis and stability properties

Numerical solution of fractional Kersten–Krasil’shchik coupled KdV–mKdV system arising in shallow water waves

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