Existence of solutions for $q$-fractional differential equations with nonlocal Erdélyi-Kober $q$-fractional integral condition

Min Jiang; Rengang Huang; Min Jiang; Rengang Huang

doi:10.3934/math.2020421

AIMS Mathematics

2020, Volume 5, Issue 6: 6537-6551. doi: 10.3934/math.2020421

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Research article

Existence of solutions for $q$-fractional differential equations with nonlocal Erdélyi-Kober $q$-fractional integral condition

Min Jiang ^{1
,
,},
Rengang Huang ²

1.
School of Data-Science and Information-Engineering, Guizhou Minzu University, Guiyang 550025, China
2.
College of Business, Guizhou Minzu University, Guiyang, 550025, China

Received: 22 June 2020 Accepted: 13 August 2020 Published: 24 August 2020
MSC : 39A13, 34B18, 34A08

In this paper, we obtain sufficient conditions for the existence, uniqueness of solutions for a fractional $q$-difference equation with nonlocal Erdélyi-Kober $q$-fractional integral condition. Our approach is based on some classical fixed point techniques, as Banach contraction principle and Schauder's fixed point theorem. Examples illustrating the obtained results are also presented.
Citation: Min Jiang, Rengang Huang. Existence of solutions for $q$-fractional differential equations with nonlocal Erdélyi-Kober $q$-fractional integral condition[J]. AIMS Mathematics, 2020, 5(6): 6537-6551. doi: 10.3934/math.2020421

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Abstract

In this paper, we obtain sufficient conditions for the existence, uniqueness of solutions for a fractional $q$-difference equation with nonlocal Erdélyi-Kober $q$-fractional integral condition. Our approach is based on some classical fixed point techniques, as Banach contraction principle and Schauder's fixed point theorem. Examples illustrating the obtained results are also presented.

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