Abstract
We apply an iterative reproducing kernel Hilbert space method to get the solutions of fractional Riccati differential equations. The analysis implemented in this work forms a crucial step in the process of development of fractional calculus. The fractional derivative is described in the Caputo sense. Outcomes are demonstrated graphically and in tabulated forms to see the power of the method. Numerical experiments are illustrated to prove the ability of the method. Numerical results are compared with some existing methods.
Highlights
1 Introduction In this work, we present an iterative reproducing kernel Hilbert spaces method (IRKHSM) for investigating the fractional Riccati differential equation of the following form [, ]: cDα +u(η) = p(η)u (η) + q(η)u(η) + r(η), ≤ η ≤ T, ( )
Fractional Riccati differential equations arise in many fields, discussions on the numerical methods for these equations are rare
We investigate the fractional Riccati differential equation as cDα +u(η) = + u(η) – u (η), ≤ η ≤ T, ( )
Summary
1 Introduction In this work, we present an iterative reproducing kernel Hilbert spaces method (IRKHSM) for investigating the fractional Riccati differential equation of the following form [ , ]: cDα +u(η) = p(η)u (η) + q(η)u(η) + r(η), ≤ η ≤ T, ( ) Odibat and Momani [ ] investigated a modified homotopy perturbation method for fractional Riccati differential equations. This useful framework has been utilized for obtaining approximate solutions to many nonlinear problems [ ]. Reproducing kernel Hilbert space theory is given in Section .
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