Employing the Limit Residual Function Method to Solve Systems of Fractional Differential Equations (European Journal of Pure and Applied Mathematics, 2025)
This study aims to solve systems of fractional differential equations analytically using a simple new technique, the limit residual function method. This method relies on coupling the residual function with the limit to produce analytical and approximate solutions within rapidly converging series forms. This technique could be an alternative to the residual power series method which is an efficient and quick-to-solve system of fractional differential equations, both linear and nonlinear, that arise in numerous physical phenomena. To illustrate the methodology and confirm its effectiveness, the study explores three different applications. The proposed algorithm's reliability and accuracy can be easily illustrated by contrasting the numerical results with the exact solutions.
Keywords: Fractional initial value problems; Fractional power series; Caputo’s derivative operator; residual function