The Banach fixed point theorem and the nonlinear alternative of Leray–Schauder type are used to investigate the existence of solutions for fractional order functional and neutral functional differential equations with infinite delay. © 2007 Elsevier Inc. All rights reserved.

We discuss the solvability of a parameter dependent cantilever-type boundary value problem. provide an existence and localization result for positive solutions via Birkhoff–Kellogg type theorem. also obtain, under additional growth conditions, upper lower bounds involved parameters. An example is presented in order to illustrate theoretical results.

in this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation$$int_{0}^{1}b(q)d^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$using a fixed point theorem in the banach algebras. this proof is given in two cases of the continuous and discontinuous function $g$, under the generalized lipschitz and caratheodory conditions.

We investigate existence and multiplicity of weak solutions for fourth-order problems involving the Leray-Lions type operators in variable exponent spaces improve a result Bonanno Chinn\`{i} (2011). use variational methods apply theorem Marano (2010).

We continue the study of stability of a type in several directions: (1) Inside a fixed model, (2) for classes of models where the compactness theorem fails and (3) for the first order case. Appropriate localizations of the order property, the independence property, and the strict order property are introduced. We are able to generalize some of the results that were known in the case of local st...

‎‎‎Recently Samet et al. introduced the notion of $alpha$-$psi$-contractive type mappings and established some fixed point theorems in complete metric spaces. In this paper, we introduce $alpha$-$(psi,varphi)$-contractive mappings and stablish coincidence and common fixed point theorems for two mapping in complete metric spaces. We present some examples to illustrate our results. As application...

Generalized Geraghty type fuzzy mappings oncomplete metric spaces are introduced and a fixed point theorem thatgeneralizes some recent comparable results for fuzzy mappings incontemporary literature is obtained. Example is provided to show thevalidity of obtained results over comparable classical results for fuzzymappings in fixed point theory. As an application, existence of coincidencefuzzy p...

Existence of solutions to some nonlinear integral equations with variable delays are obtained by the use of a fixed point theorem due to Dhage. As applications of the main results, existence results to some initial value problems concerning differential equations of higher order as well as integrodifferential equations are derived. The case of Lipschitz-type conditions is also considered. Our r...