Analytical Investigation for Some Problems Under Different Fractional Differential and Integral Operators (European Journal of Pure and Applied Mathematics, 2025)
This article presents the three well-known derivative operators—Caputo, Caputo-Fabrizio, and Atangana-Baleanu—to describe the solutions of the non-linear Fractional Partial Differential Equation (FPDE). A method called the Adomian Decomposition Method (ADM) is used to find series solutions in a semi-analytical way, using different transforms like Laplace, Elzaki, Sumudu, Aboodh, Mohand, Yang, Natural, and Shehu. The solutions obtained by the proposed method have precision and a high rate of convergence. We then verify the derived solutions numerically and graphically for both fractional and integer orders. Furthermore, the solutions under these transformations are the same. The proposed simulations show that as the number of iterations increases, the corresponding absolute error reduces. Moreover, fractional order solutions are converging to integer order solutions.
Keywords: Adomian Decomposition Method; Different Integral Transforms; Caputo Derivative Operator; Caputo-Fabrizio Derivative Operator; Atangana-Baleanu Derivative Operator