Existence of positive solution to the boundary value problems for coupled system of nonlinear fractional differential equations

Md. Asaduzzaman; Md. Zulfikar Ali; Md. Asaduzzaman; Md. Zulfikar Ali

doi:10.3934/math.2019.3.880

AIMS Mathematics

2019, Volume 4, Issue 3: 880-895. doi: 10.3934/math.2019.3.880

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Research article

Existence of positive solution to the boundary value problems for coupled system of nonlinear fractional differential equations

Md. Asaduzzaman ^{1
,
,},
Md. Zulfikar Ali ²

1.
Department of Mathematics, Islamic University, Kushtia-7003, Bangladesh
2.
Department of Mathematics, University of Rajshahi, Rajshahi-6205, Bangladesh

Received: 28 April 2019 Accepted: 11 July 2019 Published: 23 July 2019
MSC : 47H10, 34A08, 34B18, 34B18

In this paper, we investigate the existence criteria of at least one positive solution to the three-point boundary value problems with coupled system of Riemann-Liouville type nonlinear fractional order differential equations. The analysis of this study is based on the well-known Schauder's fixed point theorem. Some new existence and multiplicity results for coupled system of Riemann-Liouville type nonlinear fractional order differential equation with three-point boundary value conditions are obtained.
Citation: Md. Asaduzzaman, Md. Zulfikar Ali. Existence of positive solution to the boundary value problems for coupled system of nonlinear fractional differential equations[J]. AIMS Mathematics, 2019, 4(3): 880-895. doi: 10.3934/math.2019.3.880

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Abstract

In this paper, we investigate the existence criteria of at least one positive solution to the three-point boundary value problems with coupled system of Riemann-Liouville type nonlinear fractional order differential equations. The analysis of this study is based on the well-known Schauder's fixed point theorem. Some new existence and multiplicity results for coupled system of Riemann-Liouville type nonlinear fractional order differential equation with three-point boundary value conditions are obtained.

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