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Numerical Solution of Initial Value Problems of Time-Fractional Order via a Novel Fractional 4-Stage Runge-Kutta Method

In this article, we present a derivation of a novel 4-stage fractional Runge-Kutta method (4sFRKM). Then we apply it to solve time-fractional initial values problems. This method is useful because it provides us with good numerical solutions. When compared with the exact solution, the stability of the proposed method is examined and the corresponding region of stability is depicted. Moreover, the efficiency and accuracy of the prospected method were achieved through illustrative numerical examples, and the results are supported by tables and figures. All the calculations were done using MATLAB.