Analysis and Numerical Simulation of System of Fractional Partial Differential Equations with Non-Singular Kernel Operators

Abstract

The exact solution to fractional-order partial differential equations is usually quite difficult to achieve. Semi-analytical or numerical methods are thought to be suitable options for dealing with such complex problems. To elaborate on this concept, we used the decomposition method along with natural transformation to discover the solution to a system of fractional-order partial differential equations. Using certain examples, the efficacy of the proposed technique is demonstrated. The exact and approximate solutions were shown to be in close contact in the graphical representation of the obtained results. We also examine whether the proposed method can achieve a quick convergence with a minimal number of calculations. The present approaches are also used to calculate solutions in various fractional orders. It has been proven that fractional-order solutions converge to integer-order solutions to problems. The current technique can be modified for various fractional-order problems due to its simple and straightforward implementation.

Keywords

• Adomian decomposition method
• natural transform
• Caputo–Fabrizio (CF) and Atangana–Baleanu Caputo operator (ABC)
• fractional-order coupled systems