EXISTENCE, UNIQUENESS AND REGULARITY OF SOLUTIONS FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY

Yixing Liang; Zhenbin Fan; Gang Li

doi:10.11948/20220263

2024 Volume 14 Issue 2

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Yixing Liang, Zhenbin Fan, Gang Li. EXISTENCE, UNIQUENESS AND REGULARITY OF SOLUTIONS FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY[J]. Journal of Applied Analysis & Computation, 2024, 14(2): 623-641. doi: 10.11948/20220263

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Yixing Liang, Zhenbin Fan, Gang Li. EXISTENCE, UNIQUENESS AND REGULARITY OF SOLUTIONS FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY[J]. Journal of Applied Analysis & Computation, 2024, 14(2): 623-641. doi: 10.11948/20220263

EXISTENCE, UNIQUENESS AND REGULARITY OF SOLUTIONS FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY

1.
School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China

Author Bio: Email: lyx11252021@163.com(Y. Liang); Email: gli@yzu.edu.cn(G. Li)
Corresponding author: Email: zbfan@yzu.edu.cn(Z. Fan)

Abstract

Abstract

Within this paper, we consider the existence and uniqueness of solutions for fractional integro-differential equations with state-dependent delay on the Lipschitz continuous function space. Our results are obtained by using the resolvent operator theory and the generalized Banach contraction mapping principle. The regularity of solutions of fractional integro-differential equations with state-dependent delay is also discussed. Finally, an example is provided as an application.
- Fractional integro-differential equations /
- state-dependent delay /
- resolvent theory /
- generalized Banach contraction mapping principle
MSC: 34G20, 34K05, 45K05, 47A10

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References

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