EXISTENCE AND ASYMPTOTIC BEHAVIOR OF MILD SOLUTIONS FOR FRACTIONAL MEASURE DIFFERENTIAL EQUATIONS

Haide Gou; He Yang

doi:10.11948/20220435

2024 Volume 14 Issue 1

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Haide Gou, He Yang. EXISTENCE AND ASYMPTOTIC BEHAVIOR OF MILD SOLUTIONS FOR FRACTIONAL MEASURE DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 16-41. doi: 10.11948/20220435

Citation:

Haide Gou, He Yang. EXISTENCE AND ASYMPTOTIC BEHAVIOR OF MILD SOLUTIONS FOR FRACTIONAL MEASURE DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 16-41. doi: 10.11948/20220435

EXISTENCE AND ASYMPTOTIC BEHAVIOR OF MILD SOLUTIONS FOR FRACTIONAL MEASURE DIFFERENTIAL EQUATIONS

Haide Gou^1, ,,
He Yang^1,

1.
Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Author Bio: Email: yanghe256@163.com(H. Yang)
Corresponding author: Email: 842204214@qq.com(H. Gou)
Fund Project: The authors were supported by National Natural Science Foundation of China (Grant No. 11661071, 12061062). Science Research Project for Colleges and Universities of Gansu Province (No. 2022A-010) and Project of NWNULKQN2023-02

Abstract

Abstract

This paper is concerned with a class of nonlocal problem of multi-term time-fractional measure differential equations involving delay and nonlocal conditions in Banach spaces. We first introduce the concept of $S$-asymptotically $\omega$-periodic mild solution, on the premise of by utilizing $(\beta, \gamma_k)$-resolvent family and measure functional (Henstock-Lebesgue-Stieltjes integral) under regulated functions. And then we show by using Schauder fixed point theorem. that the existence of $S$ -asymptotically $\omega$ periodic mild solutions for the mentioned system are obtained. Finally, an example to illustrate the obtained results is given.
- Regulated functions /
- Henstock-Lebesgue-Stieltjes integral /
- fractional calculus /
- generalized semigroup theory /
- multi-term time-fractional /
- fixed point theory
MSC: 26A33, 34G20, 34K13, 47D06, 46T20

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References

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