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Research Article | Open Access

General fractional differential equations with fixed memory length

Rong-Fu Wang1, Chuan-Yun Gu1,2( )
School of Science, Xihua University, Chengdu 610039, China
School of Mathematics, Sichuan University of Arts and Science, Dazhou 635000, China
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Abstract

This paper investigated the properties and general Laplace transform of general fractional operators with fixed memory length. Subsequently, a class of general fractional differential equations with fixed memory length was systematically studied. First, the existence of solutions to this type of equations was established via integral methods. Then, the uniqueness of the solution was rigorously proven by applying the Banach fixed-point theorem.

Keywords

general Laplace transformgeneral fractional differential equationfixed memory lengthexistenceuniqueness
CLC number: 26A33, 34A08, 34A12

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AIMS Mathematics
Volume 11 Issue 4,
April 2026
Pages 10857-10882
DOI: 10.3934/math.2026446

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Wang R-F, Gu C-Y. General fractional differential equations with fixed memory length. AIMS Mathematics, 2026, 11(4): 10857-10882. https://doi.org/10.3934/math.2026446

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Received: 04 February 2026
Revised: 13 April 2026
Accepted: 15 April 2026
Published: 20 April 2026
©2026 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)