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Existence and uniqueness results for nonlinear fractional differential equations via new Q-function


In this paper, we first introduce a new concept of Q-function on partial metric spaces. Also, we give a new definition of \((\alpha ,\phi ,q)\)-contractive mapping by considering the new kind of Q-function. Then we obtain some best proximity point results for such mappings. Thus, we improve and unify many well-known results in the literature. Moreover, we provide some illustrative and nontrivial examples. Therefore, we show that the approach of Haghi et al. (Topol Appl 160:450–454, 2013) cannot be applied to our results. Finally, we obtain a solution of nonlinear fractional differential equations using the new Q-function.

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We would like to thank editor and all anonymous reviewers for their comments, which help to improve the quality of this paper.

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Correspondence to Hakan Sahin.

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Communicated by Daniel Pellegrino.

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Sahin, H. Existence and uniqueness results for nonlinear fractional differential equations via new Q-function. Adv. Oper. Theory 7, 1 (2022).

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  • Nonlinear fractional differential equations
  • Best proximity point
  • Q-function
  • \(\alpha{-}\phi \)-Contractive

Mathematics Subject Classification

  • 54H25
  • 47H10