SOLUTIONS OF LANGEVIN TYPE RIESZ-CAPUTO DIFFERENTIAL EQUATIONS IN THE FRACTIONAL SENSE UNDER ANTI-PERIODIC BOUNDARY CONDITIONS

In this article, we establish the uniqueness and existence of anti- periodic boundary value solutions for the Langevin type Riesz-Caputo differential equations in the fractional sense of the form { RCODE [RCODE+ phi] (e) = psi(rho ,Pi(rho)), (<euro> (2,3), nu <euro> (1,2], 0 <= rho <= L, Pi(0)+Pi(L) =0, Pi(0)+Pi(L)=0, Pi"(0) +Pi" (L) = 0, where RC(0)GD and RC0OD are the Riesz-Caputo fractional derivative, phi is an element of R and psi : [0, L ] X R -> R is a continuous function. Uniqueness is demonstrated using Banach's contraction principle, and existence is demonstrated employing the fixed point theorems of Schaefer and Krasnoselskii. Finally, we use several experiments to demonstrate our approaches. The software that we used is MATHEMATICA 13.3.