A note on Sobolev form fractional integro-differential equation with state-dependent delay via resolvent operators
This paper explores the new existence and uniqueness of mild solutions for a class of Sobolev form fractional integro-differential equation (in short SFFIDE) with state-dependent delay (in short SDD) and nonlocal conditions (in short NLCs) via resolvent operators in Banach spaces. By making use of Banach contraction principle and Krasnoselskii fixed point theorem (in short FPT) along with resolvent operators and fractional calculus, we develop the sought outcomes. To obtain our results, our working hypotheses are that the functions determining the equation satisfy certain Lipschitz conditions of local type. An illustration is furthermore provided to demonstrate the acquired concepts.