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Purpose: The purpose of this paper is to obtain a numerical scheme for finding numerical solutions of linear and nonlinear fractional differential equations involving ψ-Caputo derivative. Design/methodology/approach: An operational matrix to find numerical approximation of ψ-fractional differential equations (FDEs) is derived. This study extends the method to nonlinear FDEs by using quasi linearization technique to linearize the nonlinear problems. Findings: The error analysis of the proposed method is discussed in-depth. Accuracy and efficiency of the method are verified through numerical examples. Research limitations/implications: The method is simple and a good mathematical tool for finding solutions of nonlinear ψ-FDEs. The operational matrix approach offers less computational complexity. Originality/value: Engineers and applied scientists may use the present method for solving fractional models appearing in applications. [ABSTRACT FROM AUTHOR]