Work

Analysis of Implicit Neutral-Tempered Caputo Fractional Volterra–Fredholm Integro-Differential Equations Involving Retarded and Advanced Arguments

Year: 2026

Type: article

Abstract: This paper investigates a class of implicit neutral fractional integro-differential equations of Volterra–Fredholm type. The equations incorporate a tempered fractional derivative in the Caputo sense, along with both retarded (delay) and advanced arguments. The problem is formulated on a time domain segmented into past, present, and future intervals and includes nonlinear mixed integral operators. Using Banach’s contraction mapping principle and Schauder’s fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions within the space of continuous functions. The study is then extended to general Banach spaces by employing Darbo’s fixed point theorem combined with the Kuratowski measure of noncompactness. Ulam–Hyers–Rassias stability is also analyzed under appropriate conditions. To demonstrate the practical applicability of the theoretical framework, explicit examples with specific nonlinear functions and integral kernels are provided. Furthermore, detailed numerical simulations are conducted using MATLAB-based specialized algorithms, illustrating solution convergence and behavior in both finite-dimensional and Banach space contexts.

Source: Mathematics

DOI: 10.3390/math14030470

Authors: Abdulrahman A. Sharif, Muath Awadalla

Institutions: Dr. Babasaheb Ambedkar Marathwada University, Hodeidah University, King Faisal University

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funders: Deanship of Scientific Research, King Faisal University, King Faisal University