RIEMANN-LIOUVILLE FRACTIONAL INTEGRALS AND DERIVATIVES ON MORREY SPACES AND APPLICATIONS TO A
CAUCHY-TYPE PROBLEM

Jinxia Wu; Qingyan Wu; Yinuo Yang; Pei Dang; Guangzhen Ren

doi:10.11948/20230324

2024 Volume 14 Issue 2

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Article navigation > Journal of Applied Analysis & Computation > 2024 > 14(2): 1078-1096

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Jinxia Wu, Qingyan Wu, Yinuo Yang, Pei Dang, Guangzhen Ren. RIEMANN-LIOUVILLE FRACTIONAL INTEGRALS AND DERIVATIVES ON MORREY SPACES AND APPLICATIONS TO ACAUCHY-TYPE PROBLEM[J]. Journal of Applied Analysis & Computation, 2024, 14(2): 1078-1096. doi: 10.11948/20230324

Citation:

Jinxia Wu, Qingyan Wu, Yinuo Yang, Pei Dang, Guangzhen Ren. RIEMANN-LIOUVILLE FRACTIONAL INTEGRALS AND DERIVATIVES ON MORREY SPACES AND APPLICATIONS TO A CAUCHY-TYPE PROBLEM[J]. Journal of Applied Analysis & Computation, 2024, 14(2): 1078-1096. doi: 10.11948/20230324

RIEMANN-LIOUVILLE FRACTIONAL INTEGRALS AND DERIVATIVES ON MORREY SPACES AND APPLICATIONS TO A CAUCHY-TYPE PROBLEM

1.
Department of Mathematics, Linyi University, Linyi 276005, China
2.
Faculty of Innovation Engineering, Macau University of Science and Technology, Macau, China
3.
College of Science and Technology, Zhejiang International Studies University, Hangzhou 310012, China

Author Bio: Email: jinxiawu_0531@163.com(J. Wu); Email: pdang@must.edu.mo(P. Dang); Email: gzren@zisu.edu.cn(G. Ren)
Corresponding authors: Email: wuqingyan@lyu.edu.cn(Q. Wu); Email: yangyinuo1995@163.com(Y. Yang)
Fund Project: This work was partially funded by the National Natural Science Foundation of China (Grant Nos. 12171221, 12071197 and 12101564), the Natural Science Foundation of Shandong Province (Grant No. ZR2021MA031), and the National Research Foundation of Korea funded by the Ministry of Education under Grant NRF-2021R1A2C1095739

Abstract

Abstract

We investigate the boundedness and compactness of Riemann-Liouville integral operators on Morrey spaces, a class of nonseparable function spaces. Instead of adopting dual or maximal viewpoints in integrable function spaces, our approach is based on the compactness of the truncated Riemann-Liouville fractional integrals, leveraging a criterion for strongly pre-compact sets. By constructing a truncated Marchaud fractional derivative function, we characterize the solution to Abel's equation on Morrey spaces. Utilizing the fixed-point theorem, we establish the existence and uniqueness of solutions to a Cauchy-type problem for fractional differential equations. Additionally, we provide an illustrative example to demonstrate the sufficiency of the conditions presented in our main result.
- Morrey space /
- Riemann-Liouville fractional integral /
- fractional differential equation /
- fixed-point theorem
MSC: 34A08, 42B35, 34B15, 26A33

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References

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