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Analytical Representation and Applications of Solutions to a Loaded Fractional Integro-Differential Equation

Year: 2026

Type: article

Abstract: We study the Cauchy problem for a loaded fractional integro-differential equation with a time-dependent diffusion coefficient. By reducing the problem to an equivalent Volterra integral equation of the second kind, we derive explicit analytical representations of solutions under appropriate regularity assumptions. The construction of the associated resolvent kernel allows us to establish existence and uniqueness results and to investigate the role of the fractional order and the loading term in the solution structure. Two illustrative examples are presented to demonstrate the applicability of the proposed approach.

Source: Dynamics

DOI: 10.3390/dynamics6010007

Authors: Umida Baltaeva, Bobur Khasanov, Hamrobek Hayitbayev, Jamol I. Baltaev, Yolqin Alikulov

Institutions: Urgench State University, Mamun University, Urganch RANCH Texnologiya Universiteti, Tashkent University of Information Technology

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,207

OpenAlex ID: W7128922824

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