Study of time fractional proportional delayed multi‐pantograph system and integro‐differential equations

Abstract

This paper is devoted to the implementation of fractional differential transform method (FDTM) for the evaluation of new approximations for the fractional models of the system of multi-pantograph differential equations. Some new properties of FDTM have also been proposed for the fractional integro-differential equations. It is noteworthy that the integro-differential equations are studied for integers in the literature, and we have proposed the solutions of proportional delayed integro-differential equations for fractional order. The evaluated results are verified numerically by considering some test examples of fractional integro-differential equations and fractional models of the system of multi-pantograph differential equations. The outcomes conclude that evaluated series solutions via FDTM promise more appropriate approximations possess very negligible error and represent the convergent approximations. Thus, evaluated series solutions are comparatively more accurate and require less computational time. KEYWORDSfractional derivative of Caputo type, fractional differential transform method, fractional-order proportional delayed integro-differential equations, multi-pantograph system of differential equations of fractional order MSC CLASSIFICATION 34Axx, 34Kxx, 45Jxx

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