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Research Article | Open Access

On a generalized fractional integral equation of a variable-order

Department of Mathematics, College of Science, University of Hafr Al Batin, P.O. Box 1803, Hafr Al Batin 31991, Saudi Arabia
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Abstract

The paper considers a class of generalized fractional integral equations with variable-order kernels. By employing estimates based on inequalities for the Gamma function, we establish the existence and uniqueness of solutions to the proposed fractional integral equation. Furthermore, the exponential growth rate of the solution is derived using the classical retarded Gronwall inequality. Moreover, numerical and graphical illustrations of the growth estimates are presented.

Keywords

fractional integral equationswell-posednessgrowth estimatesretarded Gronwall-type inequalityfractional variable-order
CLC number: 34A06, 34A08, 35A01, 35A30, 35R11

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AIMS Mathematics
Volume 10 Issue 12,
December 2025
Pages 28295-28307
DOI: 10.3934/math.20251245

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Al Sulaimani H. On a generalized fractional integral equation of a variable-order. AIMS Mathematics, 2025, 10(12): 28295-28307. https://doi.org/10.3934/math.20251245

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Received: 01 October 2025
Revised: 18 November 2025
Accepted: 21 November 2025
Published: 02 December 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)