On solutions of fractional Riccati differential equations

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.

Implicit hybrid methods for solving fractional Riccati equation

“…The absolute errors of our results when = 0.1 and the results in[15,16,19,21] for α = 0.75. × 10 −4 4.2 × 10 −5 3.5 × 10 −6…”

“…In Table 2, we compare of the absolute errors of our results when = 0.1 and the results in [15,16,19,21] for α = 0.75. The exact solution is y (t) = t 2 .…”

Reproducing kernel Hilbert space method for solutions of a coefficient inverse problem for the kinetic equation

“…Al e'damat applied analytical-numerical method for solving a class of two-point boundary value problems [14]. For more details see [15][16][17][18][19][20][21].…”

Optimal error bound and modified kernel method for a space-fractional backward diffusion problem

“…The direct problems, i.e., initial value problem and initial boundary value problem for fractional differential equations, have been studied extensively in the past few years [15][16][17][18][19][20][21][22]. However, in some practical problems, the boundary data on the whole boundary cannot be obtained.…”