On Two-Point Boundary Value Problems and Fractional Differential Equations via New Quasi-Contractions

Maha Noorwali and Mohammed Shehu Shagari ()
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Maha Noorwali: Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Mohammed Shehu Shagari: Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria 23401, Nigeria

Mathematics, 2023, vol. 11, issue 11, 1-19

Abstract: The aim of this paper is to introduce new forms of quasi-contractions in metric-like spaces and initiate more general conditions for the existence of invariant points for such operators. The proposed notions are then applied to study novel existence criteria for the existence of solutions to two-point boundary value problems in the domains of integer and fractional orders. To attract further research in this direction, important consequences are deduced and discussed to indicate the novelty and generality of our proposed concepts.

Keywords: partial metric; metric-like; quasi-contraction; fixed point; fractional differential equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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