Genocchi collocation method for accurate solution of nonlinear fractional differential equations with error analysis

Mohamed El-gamel; Nesreen Mohamed; Waleed Adel

doi:10.53391/mmnsa.1373647

EN

Genocchi collocation method for accurate solution of nonlinear fractional differential equations with error analysis

Abstract

In this study, we introduce an innovative fractional Genocchi collocation method for solving nonlinear fractional differential equations, which have significant applications in science and engineering. The fractional derivative is defined in the Caputo sense and by leveraging fractional-order Genocchi polynomials, we transform the nonlinear problem into a system of nonlinear algebraic equations. A novel technique is employed to solve this system, enabling the determination of unknown coefficients and ultimately the solution. We derive the error bound for our proposed method and validate its efficacy through several test problems. Our results demonstrate superior accuracy compared to existing techniques in the literature, suggesting the potential for extending this approach to tackle more complex problems of critical physical significance.

Keywords

Fractional-order modelling, collocation method, nonlinear phenomena, error bound

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Details

Primary Language

English

Subjects

Numerical Analysis, Dynamical Systems in Applications

Journal Section

Research Article

Authors

Mohamed El-gamel
0000-0003-2159-6619
Egypt

Nesreen Mohamed This is me
0000-0001-5143-1837
Egypt

Waleed Adel ^*
0000-0002-0557-8536
Egypt

Publication Date

December 30, 2023

Submission Date

October 9, 2023

Acceptance Date

December 26, 2023

Published in Issue

Year 2023 Volume: 3 Number: 4

DOI

https://doi.org/10.53391/mmnsa.1373647

IZ

https://izlik.org/JA69ED33YR

APA

El-gamel, M., Mohamed, N., & Adel, W. (2023). Genocchi collocation method for accurate solution of nonlinear fractional differential equations with error analysis. Mathematical Modelling and Numerical Simulation With Applications, 3(4), 351-375. https://doi.org/10.53391/mmnsa.1373647

AMA

1.El-gamel M, Mohamed N, Adel W. Genocchi collocation method for accurate solution of nonlinear fractional differential equations with error analysis. MMNSA. 2023;3(4):351-375. doi:10.53391/mmnsa.1373647

Chicago

El-gamel, Mohamed, Nesreen Mohamed, and Waleed Adel. 2023. “Genocchi Collocation Method for Accurate Solution of Nonlinear Fractional Differential Equations With Error Analysis”. Mathematical Modelling and Numerical Simulation With Applications 3 (4): 351-75. https://doi.org/10.53391/mmnsa.1373647.

EndNote

El-gamel M, Mohamed N, Adel W (December 1, 2023) Genocchi collocation method for accurate solution of nonlinear fractional differential equations with error analysis. Mathematical Modelling and Numerical Simulation with Applications 3 4 351–375.

IEEE

[1]M. El-gamel, N. Mohamed, and W. Adel, “Genocchi collocation method for accurate solution of nonlinear fractional differential equations with error analysis”, MMNSA, vol. 3, no. 4, pp. 351–375, Dec. 2023, doi: 10.53391/mmnsa.1373647.

ISNAD

El-gamel, Mohamed - Mohamed, Nesreen - Adel, Waleed. “Genocchi Collocation Method for Accurate Solution of Nonlinear Fractional Differential Equations With Error Analysis”. Mathematical Modelling and Numerical Simulation with Applications 3/4 (December 1, 2023): 351-375. https://doi.org/10.53391/mmnsa.1373647.

JAMA

1.El-gamel M, Mohamed N, Adel W. Genocchi collocation method for accurate solution of nonlinear fractional differential equations with error analysis. MMNSA. 2023;3:351–375.

MLA

El-gamel, Mohamed, et al. “Genocchi Collocation Method for Accurate Solution of Nonlinear Fractional Differential Equations With Error Analysis”. Mathematical Modelling and Numerical Simulation With Applications, vol. 3, no. 4, Dec. 2023, pp. 351-75, doi:10.53391/mmnsa.1373647.

Vancouver

1.Mohamed El-gamel, Nesreen Mohamed, Waleed Adel. Genocchi collocation method for accurate solution of nonlinear fractional differential equations with error analysis. MMNSA. 2023 Dec. 1;3(4):351-75. doi:10.53391/mmnsa.1373647