EVALUATION OF ANALYTICAL SOLUTION FOR FRACTIONAL DIFFUSION EQUATIONS USING FIXED POINT THEOREMS AND ENHANCED ADOMIAN DECOMPOSITION METHOD

Abstract

In recent years, the diffusion equations and fixed-point theorems are considered as a main role to solve different mathematical analysis sensing. Hence in this paper, enhanced Adomian decomposition method is developed to solve the considered problems with efficient solutions. Here, the fractional diffusion equations are considered with variable coefficients to formulate the problems. The fractional integral or derivative functions are utilized with the consideration of caputo definition. This proposed approach is utilized to analysis the analytical solutions to compute the optimal solutions. Additionally, optimal solutions are obtained with the consideration of three fixed point theorems such as Arzela Ascoli theorem, Schaefer fixed point theorem and Banach fixed point theorem. The formulated problems are solved by using the enhanced Adomian decomposition method as well as fixed point theorems. In last, the numerical analysis of the considered problems with the solutions of the fixed-point theorems are presented. The proposed method is working based on iteration process to achieve the best solutions related with the considered problems. Finally, the optimal solutions of the considered problems are analyzed and validated with the proof analysis.