Series Solution of Fractional Differential Equations Describing Physical Systems - V., Keerthika; Prahalatha, R. (Communications in Mathematics and Applications, 2024)
The aim of this paper is to extend the iterative method based on the DGJM method of solving functional equations, to solve the fractional differential equations, where the order of derivative is taken in Caputo’s sense. The iterative procedure is explained and demonstrated by solving non-linear time fractional partial differential equations like Heat equation, Burger’s equation, Fokker Planck equation, Korteweg-de Vries (KdV) equation and Klien-Gordon equation. The scheme of iteration is also extended to solve the system of Drinfeld-Sokolov-Wilson equations and coupled Jaulent-Miodek equations. Graphs are used to depict the accuracy of the method and absolute errors between exact and approximate solutions are tabulated to ensure that the proposed scheme is both computationally intriguing and simple to implement.
Keywords: Non-linear fractional differential equations; Series solution; System of fractional differential equations; Decomposition technique