Title: Existence and stability analysis of neutral implicit fractional pantograph differential equations with non-local conditions using fixed-point theorems

Authors: N. Annapoorani; D. Prabu

Addresses: Department of Mathematics, Bharathiar University, Coimbatore – 641046, India ' Department of Mathematics, Sri Shakthi Institute of Engineering and Technology, Coimbatore – 62, India

Abstract: This study explores the existence and stability of solutions for implicit neutral fractional pantograph differential equations with non-local conditions, utilising the recently introduced Ψ-Caputo fractional derivative. The research is driven by the increasing interest in fractional differential equations, particularly for their effectiveness in modelling complex systems characterised by memory and hereditary effects. This work addresses significant challenges associated with the combination of neutral terms, pantograph delays, and non-local boundary conditions an area that has received limited attention in the literature despite its relevance across various applied fields. To overcome these challenges, we apply fixed-point theorems, specifically the Banach and Schaefer fixed-point theorems, to establish new existence results for the solutions of the proposed equations. Additionally, we demonstrate the Ulam-Hyers stability of the problem, ensuring that minor perturbations in the initial data result in only small deviations in the solution, thus enhancing the robustness of the model. The theoretical findings are validated through an illustrative example, highlighting the practical relevance of the results and their potential applications in modelling real-world phenomena. This study not only advances the theoretical framework of fractional differential equations but also offers valuable insights for their application across a broad range of scientific and engineering disciplines.

Keywords: non-local conditions; Ψ-Caputo fractional derivative; existence of solutions; fixed-point theorems; Ulam-Hyers stability; pantograph differential equations.

DOI: 10.1504/IJDSDE.2024.145823

International Journal of Dynamical Systems and Differential Equations, 2024 Vol.13 No.6, pp.565 - 581

Received: 24 Jul 2024
Accepted: 27 Sep 2024
Published online: 25 Apr 2025 *

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