Abstract
In this manuscript, we work to actualize the Darbo (Banas and Goebel in Measure of Noncompactness in Banach Space. Lecture Notes in Pure and Applied Mathematics, 1980) fixed point theorem (FPT) coupled with the Hausdorff measure of non-compactness to analyze the existence results for an impulsive fractional neutral integro-differential equation (IFNIDE) with state-dependent delay (SDD) and non-instantaneous impulses (NII) in Banach spaces. Finally, examples are offered to demonstrate the concept.
Highlights
Throughout this manuscript, we set up the existence of mild solutions for impulsive fractional neutral integro-differential equation (IFNIDE) with state-dependent delay (SDD) and non-instantaneous impulses (NII) in Banach spaces through the utilization of the fixed point theorem (FPT) thanks to Darbo [ ]
1 Introduction Throughout this manuscript, we set up the existence of mild solutions for IFNIDE with SDD and NII in Banach spaces through the utilization of the FPT thanks to Darbo [ ]
Kumar et al [ ] analyzed the existence of solutions for Fractional differential equations (FDE) with NII in Banach spaces through the utilization of the appropriate FPT
Summary
Throughout this manuscript, we set up the existence of mild solutions for IFNIDE with SDD and NII in Banach spaces through the utilization of the FPT thanks to Darbo [ ]. Kumar et al [ ] analyzed the existence of solutions for FDE with NII in Banach spaces through the utilization of the appropriate FPT. Later Das et al [ , ] researched the existence of mild solution of a class of second order partial neutral differential equations with SDD and NII in Banach spaces. The existence results for IFIDE with SDD and NII in Bh phase space contexts have not yet been completely examined. Let L (X) symbolize the Banach space of all bounded linear operators from X into X, having norm · L (X).
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