Numerical solution of nonlinear fractional integro-differential equation by Collocation method

Unhale, S. I.; Kendre, Subhash

doi:10.26637/mjm0601/0011

Cited by 3 publications

(1 citation statement)

References 14 publications

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“…Arshed [27] demonstrated the Bspline technique for solving linear FPIDE. Unhale and Kendre [28] presented collocation technique to solve the nonlinear FPIDE utilizing the Chebyshev polynomials and the shifted Legendre polynomials. Avazzadeh et al [29] established a hybrid technique by blending the Legendre wavelets, and operational matrix of fractional integration.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Study of Nonlinear Fractional Order Partial Integro-Differential Equation with a Weakly Singular Kernel

2021

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Fractional differential equations can present the physical pathways with the storage and inherited properties due to the memory factor of fractional order. The purpose of this work is to interpret the collocation approach for tackling the fractional partial integro-differential equation (FPIDE) by employing the extended cubic B-spline (ECBS). To determine the time approximation, we utilize the Caputo approach. The stability and convergence analysis have also been analyzed. The efficiency and reliability of the suggested technique are demonstrated by two numerical applications, which support the theoretical results and the effectiveness of the implemented algorithm.

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Section: Introductionmentioning

confidence: 99%

A Numerical Study of Nonlinear Fractional Order Partial Integro-Differential Equation with a Weakly Singular Kernel

2021

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Finite Element Method for Fractional Parabolic Integro-Differential Equations with Smooth and Nonsmooth Initial Data

Mahata

Sinha

2021

J Sci Comput

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LADM procedure to find the analytical solutions of the nonlinear fractional dynamics of partial integro-differential equations

Khan,

Kumam

et al. 2024

Demonstratio Mathematica

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Generally, fractional partial integro-differential equations (FPIDEs) play a vital role in modeling various complex phenomena. Because of the several applications of FPIDEs in applied sciences, mathematicians have taken a keen interest in developing and utilizing the various techniques for its solutions. In this context, the exact and analytical solutions are not very easy to investigate the solution of FPIDEs. In this article, a novel analytical approach that is known as the Laplace adomian decomposition method is implemented to calculate the solutions of FPIDEs. We obtain the approximate solution of the nonlinear FPIDEs. The results are discussed using graphs and tables. The graphs and tables have shown the greater accuracy of the suggested method compared to the extended cubic-B splice method. The accuracy of the suggested method is higher at all fractional orders of the derivatives. A sufficient degree of accuracy is achieved with fewer calculations with a simple procedure. The presented method requires no parametrization or discretization and, therefore, can be extended for the solutions of other nonlinear FPIDEs and their systems.

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Numerical solution of nonlinear fractional integro-differential equation by Collocation method

Cited by 3 publications

References 14 publications

A Numerical Study of Nonlinear Fractional Order Partial Integro-Differential Equation with a Weakly Singular Kernel

A Numerical Study of Nonlinear Fractional Order Partial Integro-Differential Equation with a Weakly Singular Kernel

Finite Element Method for Fractional Parabolic Integro-Differential Equations with Smooth and Nonsmooth Initial Data

LADM procedure to find the analytical solutions of the nonlinear fractional dynamics of partial integro-differential equations

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