Analysis of Caputo-Fabrizio fractional order semi-linear parabolic equations via effective amalgamated technique

The significance of semi-linear parabolic equations in various fields of physics and chemistry is perpetual. Literature is enriched with the modeling and numerical investigations of their various paradigms. In this paper, a class of semi-linear diffusion equations is considered as prototypical semi-linear parabolic equation. The equations are reformulated to fractional order derivative by applying Caputo-Fabrizio time fractional derivative (CFTFD). Moreover, an amalgamated technique, that is, a semi-analytical technique is also established, which is combination of Laplace transform and Picard's iterative method (LTPIM). Specifically, it is designed to effectively simulate the governing semi-linear diffusion equations. In addition, the stability analysis of this amalgamated technique is also carried out through comparison with Banach fixed point theorem and H-stable mapping. The obtained results are illustrated graphically and in tabulated form, which evidently validates the proficiency of this technique for semi-linear parabolic equations.

Automated summary

The paper discusses the significance of semi-linear parabolic equations in various fields, presents a class of semi-linear diffusion equations as a prototypical example, and reformulates the equations to fractional order derivatives using Caputo-Fabrizio time fractional derivative. It also introduces a semi-analytical technique, a combination of Laplace transform and Picard's iterative method, to effectively simulate the governing equations and validates its proficiency through stability analysis.