This paper is concerned with the existence of solutions for a new boundary value problem nonlinear coupled (k,?)–Hilfer fractional differential equations subject to (k,?)–Riemann–Liouville integral conditions. We prove two results by applying Leray–Schauder alternative, and Krasnosel’ski?’s fixed-point theorem under different criteria, while third result, concerning uniqueness given problem, re...

Banach contraction principle is a fundamental result in fixed point theory and has been applied and extended in many different directions. In 2002, Branciari [3] obtained a fixed point theorem for a single mapping satisfying an analogue of Banach’s contraction principle for an integral type inequality. Aliouche [2] established a common fixed point theorem for weakly compatible mappings in symme...

We obtain existence and uniqueness fixed point theorems as well approximation results for some classes of mappings defined by symmetric contractive type conditions in a convex metric space the sense Takahashi. By using new approach, i.e., technique enrichment mappings, we general which extend known Banach contraction mapping principle from spaces other corresponding enriched on spaces. To indic...

<p style='text-indent:20px;'>In this paper, we study a class of hyperbolic equations the fourth order with strong damping and logarithmic source terms. Firstly, prove local existence weak solution by using contraction mapping principle. Secondly, in potential well framework, global solutions energy decay estimate are obtained. Finally, give blow up result at finite time under subcritical ...

In this paper, we introduce the notions of fuzzy $alpha$-Geraghty contraction type mapping and fuzzy $beta$-$varphi$-contractive mapping and establish some interesting results on the existence and uniqueness of fixed points for these two types of mappings in the setting of fuzzy metric spaces and non-Archimedean fuzzy metric spaces. The main results of our work generalize and extend some known ...