Modified Atangana-Baleanu-Caputo Derivative for Non-Linear Hyperbolic Coupled System

Document Type : Original Article

Authors

1 Cairo university, faculty of science, Cairo, Egypt

2 Basic Science Department, MHIET, Minya, Egypt

3 Mathematics Department, Faculty of Science, Suez University, Suez, Egypt.

Abstract

Abstract
Fractional differential equations have drawn a lot of interest in applied mathematics and engineering over the past 20 years. In addition to being a hot topic in mathematics, fractional calculus has applications in a wide range of other fields, including engineering, chemistry, aerodynamics, control theory, physics, biology, continuum, and statistical mechanics. This fraction may be seen as a function in any variable, including time, space and other variables. Therefore, fractional derivatives authors benefit from displaying such unusual behaviors to explain various processes. Such operators reveal the distinguished characteristics of extended relationships, which the criterion integer order differential equation can’t prove.

This study presents the fractional modified Atangana-Baleanu-Caputo derivative for the solution of a non-homogeneous nonlinear coupled system of hyperbolic partial differential equations. The system has also been solved in the Atangana-Baleanu-Caputo derivative to prove that it is effective for these kinds of problems. The system has been fracted in space-time, and it has been demonstrated through research that the suggested approach is second-order convergent in both space and time and conditionally stable. The numerical method non-standard finite difference has been provided toward the conclusion to compare the exact and numerical results to the problem. The stability of the current system was explained by applying Von Neumann analysis. The effectiveness and reliability of the theoretical estimations are demonstrated by the numerical solutions.

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