MONOTONE ITERATIVE TECHNIQUE FOR FRACTIONAL MEASURE DIFFERENTIAL EQUATIONS IN ORDERED BANACH SPACE

Haide Gou

doi:10.11948/20230327

2024 Volume 14 Issue 5

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Haide Gou. MONOTONE ITERATIVE TECHNIQUE FOR FRACTIONAL MEASURE DIFFERENTIAL EQUATIONS IN ORDERED BANACH SPACE[J]. Journal of Applied Analysis & Computation, 2024, 14(5): 2673-2703. doi: 10.11948/20230327

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Haide Gou. MONOTONE ITERATIVE TECHNIQUE FOR FRACTIONAL MEASURE DIFFERENTIAL EQUATIONS IN ORDERED BANACH SPACE[J]. Journal of Applied Analysis & Computation, 2024, 14(5): 2673-2703. doi: 10.11948/20230327

MONOTONE ITERATIVE TECHNIQUE FOR FRACTIONAL MEASURE DIFFERENTIAL EQUATIONS IN ORDERED BANACH SPACE

Haide Gou^1, ,

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

Corresponding author: Email: 842204214@qq.com(H. Gou)
Fund Project: The authors were supported by the National Natural Science Foundation of China (Grant No. 11661071, 12061062). Science Research Project for Colleges and Universities of Gansu Province (No. 2022A-010). Lanzhou Youth Science and Technology Talent Innovation Project (2023-QN-106) and Project of NWNU-LKQN2023-02

Abstract

Abstract

This article is based on the monotonic iterative method in the presence of upper and lower solutions, and investigates the existence of $ S $-asymptotic $ \omega $-periodic mild solutions for a class of fractional measure differential equations with nonlocal conditions in an ordered Banach spaces. Firstly, in the case of upper and lower solutions, a monotonic iterative method is constructed to obtain the maximal and minimal $ S $-asymptotically $ \omega $-periodic mild solution to our concern problem. Secondly, we establish an existence result of $ S $-asymptotically $ \omega $-periodic mild solutions for the mentioned without assuming the existence of upper and lower $ S $-asymptotically $ \omega $-periodic mild solutions under generalized monotonic conditions and non compactness measure conditions of nonlinear terms. Finally, as an application of abstract results, an example is provided to illustrate our main findings.
- Regulated functions /
- Henstock-Lebesgue-Stieltjes integral /
- measure differential equations /
- monotone iterative technique
MSC: 26A33, 34G20, 34K37, 39A99, 46G99

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References

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