Authors: Rama Krishna Pinninti, M. Kalyani
Abstract: The extension of differentiation and integration to non-integer orders has been successfully achieved by fractional calculus, which serves as a sophisticated means of describing the dynamics of systems with memory effects or hereditary property. In this paper, we introduce a novel scheme for solving nonlinear FDEs through the use of operator theory coupled with an analytic technique. In particular, the proposed approach involves the Caputo definition of a fractional derivative and provides an elegant scheme for finding the closed-form solutions of a wide variety of nonlinear FDEs, especially focusing on the fractional Riccati equation as a model equation. It will be shown that it is possible to transform fractional-order systems into integral equations, and then apply an iterative process to find the solution of nonlinear FDEs. The numerical simulations show good agreement with the analytical solutions for different orders of fractions.
DOI: http://doi.org/10.5281/zenodo.22724368
