A Physical Phenomenon for the Fractional Nonlinear Mixed Integro-Differential Equation Using a General Discontinuous Kernel

Autor: Mohamed Abdou, Sharifah Alhazmi
Jazyk: angličtina
Rok vydání: 2023
Předmět:
Zdroj: Fractal and Fractional
Volume 7
Issue 2
Pages: 173
ISSN: 2504-3110
DOI: 10.3390/fractalfract7020173
Popis: In this study, a fractional nonlinear mixed integro-differential equation (Fr-NMIDE) is presented and has a general discontinuous kernel based on position and time space. Conditions of the existence and uniqueness of the solution is provided through the principal form of the integral equation, based on the Banach fixed point theorem. After applying the properties of a fractional integral, the Fr-NMIDE conformed to the Volterra–Hammerstein integral equation (V-HIE) of the second kind, with a general discontinuous kernel in position with the Hammerstein integral term and a continuous kernel in time to the Volterra term. Then, using a technique of the separating method, we obtained HIE, where its physical coefficients were variable in time. The Toeplitz matrix method (TMM) and its schemes were used to obtain a nonlinear algebraic system by studying the convergence of the system. The Maple 18 program was implemented to present the numerical results, along with corresponding errors.
Databáze: OpenAIRE
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