On a generalized fractional integral equation of a variable-order

Hamdan Al Sulaimani; Hamdan Al Sulaimani

doi:10.3934/math.20251245

AIMS Mathematics

2025, Volume 10, Issue 12: 28295-28307. doi: 10.3934/math.20251245

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Research article

On a generalized fractional integral equation of a variable-order

Hamdan Al Sulaimani ^,

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

Received: 01 October 2025 Revised: 18 November 2025 Accepted: 21 November 2025 Published: 02 December 2025
MSC : 34A06, 34A08, 35A01, 35A30, 35R11

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.
- fractional integral equations,
- well-posedness,
- growth estimates,
- retarded Gronwall-type inequality,
- fractional variable-order
Citation: Hamdan Al Sulaimani. On a generalized fractional integral equation of a variable-order[J]. AIMS Mathematics, 2025, 10(12): 28295-28307. doi: 10.3934/math.20251245

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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.

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