On the existence of solutions to psi-Hilfer fractional neutral integro-differential equations with delay

Vinitha Ravi; Nirmalkumar Rajendran; Shyamsunder

doi:10.24193/subbmath.2026.2.01

Authors

Vinitha Ravi Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore–641020, India https://orcid.org/0009-0003-2383-9001
Nirmalkumar Rajendran Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore–641020, India https://orcid.org/0000-0003-1348-6049
Shyamsunder Department of Mathematics, SRM University Delhi-NCR, Sonepat–131029, Haryana, India https://orcid.org/0000-0002-8020-0541

DOI:

https://doi.org/10.24193/subbmath.2026.2.01

Keywords:

$\Psi$-Hilfer fractional derivative, fractional integro-differential equations, existence and uniqueness, Ulam-Hyers Stability

Abstract

This paper investigates a class of neutral-type fractional differential equations with finite delays, formulated through the generalized psi-Hilfer fractional derivative. This operator, being a broad framework that unifies various fractional derivatives, is highly effective in modeling dynamical processes with memory and hereditary characteristics. The primary objective is to establish sufficient conditions for the existence and uniqueness of solutions to such equations. The analysis employs fixed point theory—specifically Banach’s contraction principle and Krasnoselskii’s fixed point theorem—within an appropriately weighted function space. These tools ensure that the solutions are not only well-defined but also uniquely determined. Furthermore, two stability notions, namely Ulam–Hyers stability and its generalized form, are studied to verify that solutions remain close to the expected behavior under small perturbations in initial conditions or parameters. To demonstrate the applicability of the theoretical framework, an illustrative example with explicit functions and parameters is provided. The results strengthen the theoretical foundations of fractional calculus and open directions for further research on more generalized and complex delayed fractional systems.

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