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Existence results for ABC-fractional BVP via new fixed point results of F-Lipschitzian mappings

Mehmood Nayyar, Khan Israr Ali, Nawaz Muhammad Ayyaz, Ahmad Niaz

Demonstratio Mathematica

2022

Vol. 55, nr 1

452--469

In this article, fixed point results for self-mappings in the setting of two metrics satisfying F -lipschitzian conditions of rational-type are proved, where F is considered as a semi-Wardowski function with constant τ∈R instead of τ>0 . Two metrics have been considered, one as an incomplete while the other is orbitally complete. The mapping is taken to be orbitally continuous from one metric to another. Some examples are provided to validate our results. For applications, we present existence results for the solutions of a new type of ABC-fractional boundary value problem.