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

Abstract

This article deals with the investigation concerning the existence and uniqueness of anti-periodicboundary value solutions for a kind of Riesz-Caputo fractional differential equations\begin{align*}&{ }_{0}^{R C} D_{l}^{\zeta} \varpi(\tau)+\mathfrak{T}\left(\tau, \varpi(\tau),{ }_{0}^{R C} D_{l}^{\varsigma} \varpi(\tau)\right)=0, \tau \in \mathcal{J}:=[0, l], \\ & a_{1} \varpi(0)+b_1\varpi(l)=0, a_{2}\varpi ^{\prime}(0)+b_{2} \varpi^{\prime}(l)=0, a_{3} \varpi^{\prime \prime}(0)+b_{3} \varpi^{\prime \prime}(l)=0\end{align*}where $2<\zeta \leq 3$ and, $1<\varsigma \leq 2,{ }_{0}^{R C} D_{l}^{\kappa}$is the Riesz-Caputo fractional derivative of order $\kappa \in\{\zeta, \varsigma\}$,$\mathfrak{T}: \mathcal{J} \times \mathbb{R} \times \mathbb{R} \rightarrow \mathbb{R}$ is a continuous function, and $a_i, b_i$ are non-negative constants with $a_i>b_i$, $i=1,2,3$. Our results are supported by suitable numerical illustrations.