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Pata type contractions involving rational expressions with an application to integral equations

  • * Corresponding author: Erdal Karapınar

    * Corresponding author: Erdal Karapınar 
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  • In this paper, we introduce the notion of rational Pata type contraction in the complete metric space. After discussing the existence and uniqueness of a fixed point for such contraction, we consider a solution for integral equations.

    Mathematics Subject Classification: Primary: 54H25, 47H10; Secondary: 54E50.

    Citation:

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    [2] A. Ali, K. Shah, F. Jarad, V. Gupta and T. Abdeljawad, Existence and stability analysis to a coupled system of implicit type impulsive boundary value problems of fractional-order differential equations, Adv. Difference Equ., (2019), Article Number 101, 21 pp. doi: 10.1186/s13662-019-2047-y.
    [3] A. Atangana, Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties, Phys. A, 505 (2018), 688-706.  doi: 10.1016/j.physa.2018.03.056.
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    [12] E. Karapinar, T. Abdeljawad and F. Jarad, Applying new fixed point theorems on fractional and ordinary differential equations, Adv. Difference Equ., 2019 (2019), Paper No. 421, 25 pp. doi: 10.1186/s13662-019-2354-3.
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