Solutions of Riesz-Caputo fractional derivative problems involving anti-periodic boundary conditions

This article deals with the investigation concerning the existence and uniqueness of anti-periodic boundary value solutions for a kind of Riesz-Caputo fractional differential equations. The equation is as follows (RC) (0) D (zeta) (l) Pi(tau) + T tau, Pi(tau), (RC) D-0(l)eta Pi ( tau )= 0 , tau is an element of J := [0, l ] , a(1) Pi (0) + b(1) Pi ( l ) = 0, a(2) Pi ' (0) + b2 Pi ' ( l ) = 0, a(3)Pi '' (0) + b(3) Pi '' ( l ) = 0, where 2 < zeta <= 3 and, 1 < eta <= 2, (RC) (0) D kappa l is the Riesz-Caputo fractional derivative of order kappa is an element of {zeta, eta}, T : J x R x R -> R is a continuous function and a i , b(i) are non-negative constants with a(i) > b(i) , i = 1, 2, 3. Uniqueness is demonstrated using Banach contraction principle, and existence is demonstrated employing the fixed point theorems of Schaefer and Krasnoselskii. Our results are supported by suitable numerical illustrations.