In this paper, the Mamadu Decomposition Transform Method (MDTM) is developed and implemented for the solution of the time-space fractional telegraph equation using the Mittag-Leffler function. The MDTM is a hybrid analytic-numerical technique designed to resolve complex differential equations, requiring no form of domain discretization, thereby reducing computational cost and complexity. The MDTM integrates the Mamadu Transform and Adomian Decomposition Method (ADM) to obtain reliable, accurate, and efficient solutions. The method (MDTM) is experimented on with the proposed problem by varying the parameters α, β, and µ. Resulting numerical evidence obtained from MDTM is compared with the analytic solution expressed using the Mittag-Leffler function and other methods in literature, such as the Adomian Decomposition Method (ADM), Homotopy Analysis Method (HAM), Homotopy Perturbation Method (HPM), Finite Difference Method (FDM), Fractional Differential Transform Method (FDTM), and Spectral Tau Method, for demonstrating effectiveness, accuracy, and excellent convergence. The finding reflects the effectiveness and efficiency of MDTM in resolving fractional order telegraph equations, making it a viable tool for resolving other Partial Differential Equations (PDEs).

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E.J. Mamadu, J.C. Nwankwo, I.S.O. Emmanuel, M.A. Ebikonbo-Owei and I.N. Njoseh “Mamadu Decomposition Transform Method for Time-Space Fractional Telegraph Equation with Mittag-Leffler function” International Journal of Applied and Physical Sciences, vol. 11, pp. 16-28, 2025. Doi: https://dx.doi.org/10.20469/ijaps.11.50003