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Existence of weak solutions for ψ-Caputo fractional boundary value problem via variational methods
adnan khaliq,Mujeeb ur Rehman
Keywords:ψ-Caputo fractional differential operator, weak solution, critical point theory.
Abstract:
      This article is about a ψ-Caputo fractional boundary value problem which is investigated with the help of variational methods and critical point theory. A touchstone is obtained on the existence of the solution of the problem with the help of a functional. The problem is reduced into an equivalent form such that the solutions of the problem coincide with the critical points of a functional. Using aid from the critical point theory, sufficient conditions are obtained for the existence of at least one solution. In the end, an example is also given to enrich our results.