Abstract
In this paper, we broaden the utilization of a beautiful computational scheme, residual power series method (RPSM), to attain the fractional power series solutions of nonhomogeneous and homogeneous nonlinear time-fractional systems of partial differential equations. This paper considers the fractional derivatives of Caputo-type. The approximate solutions of given systems of equations are calculated through the utilization of the provided initial conditions. This iterative scheme generates the fast convergent series solutions with conveniently determinable components. The implementation of this numerical scheme clearly exhibits its effectiveness, reliability and easiness regarding the procedure of the solution, as well as its better approximation. The repercussions of the fractional order of Caputo derivatives on solutions are depicted through graphical presentations for various particular cases.
Highlights
Physical phenomena of the miscellaneous fields of engineering and science can be modelled very appropriately by utilizing fractional partial differential equations (FPDEs)
This paper presents the execution of residual power series method (RPSM) to compute the fractional power series (FPS) solutions of nonhomogeneous and homogeneous nonlinear systems of FPDEs arising in physical sciences as given below: Problem 1 Solve the nonhomogeneous nonlinear fractional system
This paper significantly presents the implementation of the RPSM to the systems of PDEs of nonlinear nature with Caputo fractional derivatives
Summary
Physical phenomena of the miscellaneous fields of engineering and science can be modelled very appropriately by utilizing fractional partial differential equations (FPDEs). The theory of fractional calculus is equipped with fantastic tools to describe the dynamical behaviour, and memory related characteristics of scientific systems and processes. Various authors have used fractional differential equations (FDEs) in the modelling and analysis of scientific phenomena in different fields of knowledge [1,2,3]. The theory of fractional calculus has been widely utilized in various fields and it is growing very fast in developing models due to its relation with memory and fractals which are abundant in real physical systems. Fractional order modelling minimizes the inaccuracy that arises from the ignorance of significant real parameters. It permits a greater degree of freedom in the model compared to an integer-order system. FDEs are equipped with magnificent techniques for the characterization of hereditary and memory characteristics
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