*Correspondence: [email protected] 1College of Mathematics and Statistics, Hefei Normal University, Hefei, 230061, P.R. China 2College of Mathematical Science, University of Science and Technology of China, Hefei, 230000, P.R. China Abstract This work deals with a boundary value problem for a nonlinear multi-point fractional differential equation on the infinite interval. By constructing the p...

The current paper intends to report the existence and uniqueness of positive solutions for nonlinear pantograph Caputo–Hadamard fractional differential equations. As part a procedure, we transform specified equation into an equivalent integral equation. We show that this has solution by utilising Schauder fixed point theorem (SFPT) upper lower method. Another method proving singular is Banach (...

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...

and Applied Analysis 3 Let E be a real Banach space with a cone K. K introduces a partial order ≤ in E as x ≤ y if y − x ∈ K. Definition 2.1. For x, y ∈ E, the order interval 〈x, y〉 is defined as 〈 x, y 〉 { z ∈ E : x ≤ z ≤ y. 2.1 Theorem 2.2 Leray-Schauder Theorem 17 . Let E be a Banach space with C ⊆ E closed and convex. Assume U is relatively open subset of C with 0 ∈ U and F : U → C is a con...

in this paper, we introduce intuitionistic fuzzy contraction mappingand prove a fixed point theorem in intuitionistic fuzzy metric spaces.

This paper presents a Banach space based approach towards a denotational semantics of a probabilistic constraint programming language. This language is based on the concurrent constraint programming paradigm, where randomness is introduced by means of a probabilis-tic choice construct. As a result, we obtain a declarative framework, in which randomised algorithms can be expressed and formalised...

although homotopy-based methods, namely homotopy analysis method andhomotopy perturbation method, have largely been used to solve functionalequations, there are still serious questions on the convergence issue of thesemethods. some authors have tried to prove convergence of these methods, butthe researchers in this article indicate that some of those discussions are faulty.here, after criticizi...

In this paper, we prove a general fixed point theorem in $textrm{S}$-metric spaces for maps satisfying an implicit relation on complete metric spaces. As applications, we get many analogues of fixed point theorems in metric spaces for $textrm{S}$-metric spaces.

In this paper, we establish some existence results for higher-order nonlinear fractional differential inclusions with multi-strip conditions, when the right-hand side is convex-compact as well nonconvexcompact values. First, use alternative of Leray-Schauder type multivalued maps. We investigate next result by using well-known Covitz and Nadler?s fixed point theorem contractions. The are illust...

In this paper, using Caputo-Fabrizio fractional derivative, we obtain some new results for the existence and uniqueness of solutions differential equation with nonlocal initial value about order 0 < ? 1 . These are applied help Arzela-Ascoli theorem Schauder fixed point. Also based on ?-contractive maps such problems, unique has been introduced proved. Finally, illustrative example is consid...