Research article

Fractional convex type contraction with solution of fractional differential equation

  • 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.

    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

    Related Papers:

  • 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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