On the Solutions of the Higher Order Fractional Differential Equations of Riesz Space Derivative with Anti-Periodic Boundary Conditions

Abstract

We present existence and uniqueness results for a class of higher order anti-periodic fractional boundary value problems with Riesz space derivative which is two-sided fractional operator. The obtained results are established by applying some fixed point theorems. Various numerical examples are given to illustrate the obtained results.

Controlled Extended Branciari Quasi-b-Metric Spaces, Results, and Applications to Riesz-Caputo Fractional Differential Equations and Nonlinear Matrix Equations

“…In the anomalous diffusion problem, for example, the Riesz fractional derivative has been utilized to account for memory effects in both past and future concentrations. The authors of [24][25][26] addressed the solution of Riesz-Caputo fractional type BVP.…”

“…Denote Λ := {K ∈ P n : ∥K∥ ≤ M} as being a closed subset of P n . According to (2), any solution of (26) in Λ has to be PD. For any K ∈ Λ, we have…”

Existence of solutions for fractional boundary value problems with Riesz space derivative and nonlocal conditions

“…Geometric and physical interpretation of fractional differentiation and integration can be found in the paper [23]. Very recently, the existence of the solutions for fractional differential equations have attracted a good deal of attention and have been developed by many authors; see the books [17,22,19] and papers [1,2,3,12,11,16,33,25,26,27,30,28,29] and the references therein. A large number of studies on fractional differential equations has been presented for the existence and uniqueness of initial value problems.…”