General fractional differential equations with fixed memory length

Rong-Fu Wang; Chuan-Yun Gu; Rong-Fu Wang; Chuan-Yun Gu

doi:10.3934/math.2026446

AIMS Mathematics

2026, Volume 11, Issue 4: 10857-10882. doi: 10.3934/math.2026446

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Research article

General fractional differential equations with fixed memory length

Rong-Fu Wang ¹,
Chuan-Yun Gu ^{1,2
,
,}

1.
School of Science, Xihua University, Chengdu 610039, China
2.
School of Mathematics, Sichuan University of Arts and Science, Dazhou 635000, China

Received: 04 February 2026 Revised: 13 April 2026 Accepted: 15 April 2026 Published: 20 April 2026
MSC : 26A33, 34A08, 34A12

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.
- general Laplace transform,
- general fractional differential equation,
- fixed memory length,
- existence,
- uniqueness
Citation: Rong-Fu Wang, Chuan-Yun Gu. General fractional differential equations with fixed memory length[J]. AIMS Mathematics, 2026, 11(4): 10857-10882. doi: 10.3934/math.2026446

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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.

References

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