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Solving mixed Volterra–Fredholm integro-differential equations: A Rishi transform-based approach

Year: 2026

Type: article

Abstract: This paper presents a novel analytical method for solving mixed Volterra–Fredholm integro-differential equations (MVFIDEs) using the recently introduced Rishi transform. These equations frequently arise in modeling complex phenomena in physics, engineering, and applied sciences, where both memory (Volterra) and global interaction (Fredholm) effects are present. We focus on deriving exact solutions without the need for iterative or purely numerical schemes. The proposed technique simplifies MVFIDEs by transforming them into algebraic equations using the operational rules and properties of the Rishi transform. Some analytical examples are presented to illustrate the complete procedure for determining the solution. In particular, we consider MVFIDEs that apply the Rishi Transform to reduce the integro-differential equation into an algebraic form involving the transform parameters ϑ and φ.

Source: AIP Advances

DOI: 10.1063/5.0307763

Authors: Hiwa Abdullah Rasol, Azhi Sabir Mohammed, Surme Rasul Saber, Awder Rasul Braim

Institutions: University of Raparin, Raparin Technical and Vocational Institute, Koya University

Language: English

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,350

OpenAlex ID: W7153132882

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Cites: 16

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