Residual Power Series Method for ψ-Caputo Fractional Differential Equations

In this paper, linear ψ-Caputo fractional differential equations with constant coefficients and initial conditions are considered. The classic residual power series method is adapted to ψ-Caputo fractional differential equations. An approximate analytical solution of the problem is written as a power series in terms of the function ψ with unknown coefficients. The method can also be applied to the ψ-Caputo fractional relaxation-oscillation equations. Numerical examples substantiate both the scope of applicability and the level of accuracy achieved by the method.