Fractional convex type contraction with solution of fractional differential equation

Aftab Hussain; Aftab Hussain

doi:10.3934/math.2020344

AIMS Mathematics

2020, Volume 5, Issue 5: 5364-5380. doi: 10.3934/math.2020344

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Research article

Fractional convex type contraction with solution of fractional differential equation

Aftab Hussain ^{1,2
,
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1.
Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
2.
Department of Mathematics, Facutly of Natural Science, Khawaja Fareed University of Engineering and Technology, Rahim Yar Khan 64200, Pakistan

Received: 16 March 2020 Accepted: 04 May 2020 Published: 22 June 2020
MSC : 47H09, 47H10, 54H25

The focus of this paper is to present a new idea of fractional convex type contraction and establish some new results for such contraction under the improved approach of fractional convex type contractive condition in the context of $\mathcal{F}$ -complete $\mathcal{F}$ -metric space. The authors derive some results for Suzuki type contractions, orbitally T-complete and orbitally continuous mappings in $\mathcal{F}$ -metric spaces and obtain some consequences by using graphic contraction. The motivation of this paper is to observe the solution of fractional order differential equation with one of the boundary condition using fixed point technique in $\mathcal{F}$ -metric space.
- fractional convex α-η-contraction,
- $\mathcal{F}$ -metric space,
- $\mathcal{F}$ -Cauchy,
- $\mathcal{F}$ -complete
Citation: Aftab Hussain. Fractional convex type contraction with solution of fractional differential equation[J]. AIMS Mathematics, 2020, 5(5): 5364-5380. doi: 10.3934/math.2020344

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Abstract

The focus of this paper is to present a new idea of fractional convex type contraction and establish some new results for such contraction under the improved approach of fractional convex type contractive condition in the context of $\mathcal{F}$ -complete $\mathcal{F}$ -metric space. The authors derive some results for Suzuki type contractions, orbitally T-complete and orbitally continuous mappings in $\mathcal{F}$ -metric spaces and obtain some consequences by using graphic contraction. The motivation of this paper is to observe the solution of fractional order differential equation with one of the boundary condition using fixed point technique in $\mathcal{F}$ -metric space.

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