Semi-analytic solutions of nonlinear multidimensional fractional differential equations

M. Botros; E. A. A. Ziada; I. L. EL-Kalla; M. Botros; E. A. A. Ziada; I. L. EL-Kalla

doi:10.3934/mbe.2022623

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 12: 13306-13320. doi: 10.3934/mbe.2022623

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Semi-analytic solutions of nonlinear multidimensional fractional differential equations

1.
Basic Science Departement, Faculty of Engineering, Delta Universiry for Science and Technology, P. O. Box 11152, Mansoura, Egypt
2.
Nile Higher Institute for Engineering and Technology, Mansoura, Egypt
3.
Mathematics and Engineering Physics Department, Faculty of Engineering, Mansoura University, Mansoura, Egypt

Academic Editor: Feliz Manuel Barrão Minhós

Received: 29 July 2022 Revised: 31 August 2022 Accepted: 02 September 2022 Published: 13 September 2022

In this paper, the Adomian decomposition method (ADM) and Picard technique are used to solve a class of nonlinear multidimensional fractional differential equations with Caputo-Fabrizio fractional derivative. The main advantage of the Caputo-Fabrizio fractional derivative appears in its non-singular kernel of a convolution type. The sufficient condition that guarantees a unique solution is obtained, the convergence of the series solution is discussed, and the maximum absolute error is estimated. Several numerical problems with an unknown exact solution are solved using the two techniques. A comparative study between the two solutions is presented. A comparative study shows that the time consumed by ADM is much smaller compared with the Picard technique.
- Adomian decomposition,
- Picard method,
- Caputo-Fabrizo,
- multidimensional,
- fractional differential equations,
- bassset problem
Citation: M. Botros, E. A. A. Ziada, I. L. EL-Kalla. Semi-analytic solutions of nonlinear multidimensional fractional differential equations[J]. Mathematical Biosciences and Engineering, 2022, 19(12): 13306-13320. doi: 10.3934/mbe.2022623

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Abstract

In this paper, the Adomian decomposition method (ADM) and Picard technique are used to solve a class of nonlinear multidimensional fractional differential equations with Caputo-Fabrizio fractional derivative. The main advantage of the Caputo-Fabrizio fractional derivative appears in its non-singular kernel of a convolution type. The sufficient condition that guarantees a unique solution is obtained, the convergence of the series solution is discussed, and the maximum absolute error is estimated. Several numerical problems with an unknown exact solution are solved using the two techniques. A comparative study between the two solutions is presented. A comparative study shows that the time consumed by ADM is much smaller compared with the Picard technique.

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