Abstract
This manuscript is devoted to presenting an approximation method based upon a new set of fractional functions named fractional-order Mittag–Leffler functions (FM-LFs). This scheme is implemented to approximate the solution of a multi-dimensional fractional pantograph differential equation. To this approach, FM-LFs are introduced. Then, we employ FM-LFs to construct the pseudo-operational matrix of fractional integration and pantograph operational matrix (P-OM). We reduce the considered problems to systems of algebraic equations with the help of the mentioned matrices, and the collocation technique, respectively. Error analysis is proposed. Moreover, several numerical experiments have been considered to confirm the efficiency and applicability of the suggested scheme.
Published Version
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