Semi-Analytical Solutions for Some Types of Nonlinear Fractional-Order Differential Equations Based on Third-Kind Chebyshev Polynomials

Author:

El-Sayed Adel Abd Elaziz12ORCID,Boulaaras Salah3ORCID,AbaOud Mohammed4ORCID

Affiliation:

1. Department of Mathematics, Faculty of Science, Fayoum University, Fayoum 63514, Egypt

2. Department of Mathematics, College of Education, University of Technology and Applied Sciences, Al-Rustaq 329, Oman

3. Department of Mathematics, College of Sciences and Arts in ArRass, Qassim University, Buraydah 51452, Saudi Arabia

4. Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia

Abstract

Approximate solutions for a family of nonlinear fractional-order differential equations are introduced in this work. The fractional-order operator of the derivative are provided in the Caputo sense. The third-kind Chebyshev polynomials are discussed briefly, then operational matrices of fractional and integer-order derivatives for third-kind Chebyshev polynomials are constructed. These obtained matrices are a critical component of the proposed strategy. The created matrices are used in the context of approximation theory to solve the stated problem. The fundamental advantage of this method is that it converts the nonlinear fractional-order problem into a system of algebraic equations that can be numerically solved. The error bound for the suggested technique is computed, and numerical experiments are presented to verify and support the accuracy and efficiency of the proposed method for solving the class of nonlinear multi-term fractional-order differential equations.

Funder

Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Reference47 articles.

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3. Baleanu, D., Balas, V.E., and Agarwal, P. (2023). Fractional Order Systems and Applications in Engineering, Academic Press.

4. Piotrowska, E., and Rogowski, K. (2021). Time-Domain analysis of fractional electrical circuit containing two ladder elements. Electronics, 10.

5. Space-fractional heat transfer analysis of hybrid nanofluid along a permeable plate considering inclined magnetic field;Khazayinejad;Sci. Rep.,2022

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