Measure of non-compactness for nonlocal boundary value problems via $ (k, \psi) $-Riemann-Liouville derivative on unbounded domain

Aphirak Aphithana; Weerawat Sudsutad; Jutarat Kongson; Chatthai Thaiprayoon; Aphirak Aphithana; Weerawat Sudsutad; Jutarat Kongson; Chatthai Thaiprayoon

doi:10.3934/math.20231020

AIMS Mathematics

2023, Volume 8, Issue 9: 20018-20047. doi: 10.3934/math.20231020

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Measure of non-compactness for nonlocal boundary value problems via $ (k, \psi) $-Riemann-Liouville derivative on unbounded domain

1.
Faculty of Engineering Science and Technology, Suvarnabhumi Institute of Technology, Samut Prakan 10540, Thailand
2.
Theoretical and Applied Data Integration Innovations Group, Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand
3.
Research Group of Theoretical and Computational Applied Science, Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand

Received: 14 December 2022 Revised: 07 May 2023 Accepted: 15 May 2023 Published: 16 June 2023
MSC : 26A33, 34A08, 34B40, 47H08, 47H10

In this paper, we investigate the existence result for $ (k, \psi) $-Riemann-Liouville fractional differential equations via nonlocal conditions on unbounded domain. The main result is proved by applying a fixed-point theorem for Meir-Keeler condensing operators with a measure of noncompactness. Finally, two numerical examples are also demonstrated to confirm the usefulness and applicability of our theoretical results.
Citation: Aphirak Aphithana, Weerawat Sudsutad, Jutarat Kongson, Chatthai Thaiprayoon. Measure of non-compactness for nonlocal boundary value problems via $ (k, \psi) $-Riemann-Liouville derivative on unbounded domain[J]. AIMS Mathematics, 2023, 8(9): 20018-20047. doi: 10.3934/math.20231020

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Abstract

In this paper, we investigate the existence result for $ (k, \psi) $-Riemann-Liouville fractional differential equations via nonlocal conditions on unbounded domain. The main result is proved by applying a fixed-point theorem for Meir-Keeler condensing operators with a measure of noncompactness. Finally, two numerical examples are also demonstrated to confirm the usefulness and applicability of our theoretical results.

References

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