EXISTENCE RESULTS OF HILFER FRACTIONAL STOCHASTIC PANTOGRAPH DIFFERENTIAL EQUATIONS WITH NON-INSTANTANEOUS IMPULSES VIA CONDENSING OPERATOR THEORY

In this study, we establish the existence of mild solutions for fractional stochastic pantograph differential equations incorporating the Hilfer fractional derivative and non-instantaneous impulses. The analysis is conducted using tools from fractional calculus, semigroup theory, and stochastic analysis under appropriate conditions. Additionally, we employ condensing operator theory, the Hausdorff measure of noncompactness, and Sadovskii's fixed point theorem to derive our existence results. A detailed example, supported by graphical analysis, is presented to illustrate the practical applicability of the theoretical findings.