Fractional calculus of interval-valued functions on time scales

Abstract

This paper aims to develop fractional interval-valued calculus on time scales that unify the continuous and discrete cases. The definitions of fractional interval-valued calculus, which encompass the integral, Riemann–Liouville (R-L) derivative, and Caputo derivative of nabla type, are established within the framework of time scales. Moreover, some fundamental properties and nabla Laplace transform of these new operators are discussed. Based on these findings, explicit solutions of several nabla fractional interval-valued differential equations on time scales are presented.