A Countable System of Fractional Inclusions with Periodic, Almost, and Antiperiodic Boundary Conditions

Abstract

This article is dedicated to the existence results of solutions for boundary value problems of inclusion type. We suggest the infinite countable system to fractional differential inclusions written by ${}_{\text{ABC}}{{\displaystyle D}}^{\alpha }\left[{\nu }_i\left(t\right)\right]\in {\mathcal{Y}}_i\left(t,{\left\{{\nu }_i\left(t\right)\right\}}_{i=1}^{\infty }\right)$ . The mappings ${\mathcal{y}}_i\left(t,{\left\{{\nu }_i\left(t\right)\right\}}_{i=1}^{\infty }\right)$ are proposed to be Lipschitz multivalued mappings. The results are explored according to boundary condition $\sigma {\nu }_i\left(0\right)=\gamma {\nu }_i\left(\rho \right),\hspace{1em}\sigma ,\gamma \in ℝ$ . This type of condition is the generalization of periodic, almost, and antiperiodic types.