Existence results for a fractional boundary value problem with fractional Lidstone conditions

Our aim in this work is to study the existence of solutions for a fractional Lidstone boundary value problems. We use some fixed point theorems to show the existence and uniqueness of solution under suitable conditions. Two examples are given to ilustrate the obtained results.     

Anti-periodic BVP of fractional order with fractional impulsive conditions and variable parameter

In this paper, by using two fixed point theorems, we discuss two classes of anti-periodic BVP for fractional differential equations with fractional impulsive conditions and variable parameter. The existence of solutions is obtained. Examples are also given to illustrate our theoretical results.     

Positive solutions of fractional differential equations with the Riesz space derivative

A new class of fractional differential equations with the Riesz–Caputo derivative is proposed and the physical meaning is introduced in this paper. The boundary value problem is investigated under some conditions. Leray–Schauder and Krasnoselskii’s fixed point theorems in a cone are adopted. Existence of positive solutions is provided. Finally, two examples with numerical solutions are given to support theoretical results.     

Existence Results for Fractional Differential Equations with the Riesz-Caputo Derivative

In this paper, we apply some fixed point theorems to attain the existence of solutions for fractional differential equations with the space-time Riesz-Caputo derivative. We study the boundary value problems that the nonlinearity term $f$ is relevant to fractional integral and fractional derivative. In addition, the boundary conditions involve integral. Two examples are given to show the effectiveness of theoretical results.     

Strong convergence theorems for monotone mappings and relatively weak nonexpansive mappings

In this paper, we prove strong convergence theorems to a zero of monotone mapping and a fixed point of relatively weak nonexpansive mapping. Moreover, strong convergence theorems to a point which is a fixed point of relatively weak nonexpansive mapping and a solution of a certain variational problem are proved under appropriate conditions.     

Existence results for fractional functional differential equations with impulses

In this paper, we discuss some existence results for a class of multi-point boundary value problem for impulsive fractional functional differential equations. Some sufficient conditions are obtained by using suitable fixed point theorems. Examples are also given to illustrate our results.     

Optimal Solutions of Fractional Nonlinear Impulsive Neutral Stochastic Functional Integro-Differential Equations

Abstract

In this article, we consider a new class of fractional impulsive neutral stochastic functional integro-differential equations with infinite delay in Hilbert spaces. First, by using stochastic analysis, fractional calculus, analytic α-resolvent operator and suitable fixed point theorems, we prove the existence of mild solutions and optimal mild solutions for these equations. Second, the existence of optimal pairs of system governed by fractional impulsive partial stochastic integro-differential equations is also presented. The results are obtained under weaker conditions in the sense of the fractional power arguments. Finally, an example is given for demonstration.     

Existence and Uniqueness of Solutions and Lyapunov-type Inequality for a Mixed Fractional Boundary Value Problem

In this paper, a Lyapunov-type inequality for a linear differential equation involving right Riemann-Liouville and left Caputo fractional derivatives under Sturm-Liouville boundary conditions is established. Furthermore, the existence of solutions for the corresponding nonlinear differential equation is obtained by fixed point theorems.     

Common fixed points of strict contractions in Menger spaces

The aim of this paper is to prove some common fixed point theorems under certain strict contractive conditions for mappings sharing the common property (E.A) in Menger spaces. As applications to our results, we obtain the corresponding common fixed point theorems under strict contraction in metric spaces. Thus, our results generalize many known results in Menger as well as metric spaces. Some related results are also derived besides presenting several illustrative examples.     

Existence and uniqueness of positive solution for nonlinear fractional q-difference equation with integral boundary conditions

This paper studies a class of nonlinear fractional $q$-difference equations with integral boundary conditions. By exploiting the properties of Green"s function and two fixed point theorems for a sum operator, the existence and uniqueness of positive solutions for the boundary value problem are established. Iterative schemes for approximating the solutions are also obtained. Explicit examples are given to illustrate main results.     

Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces

In this paper, we introduce the concept of tripled fixed point for nonlinear mappings in partially ordered complete metric spaces and obtain existence, and existence and uniqueness theorems for contractive type mappings. Our results generalize and extend recent coupled fixed point theorems established by Gnana Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (7) (2006) 1379-1393]. Examples to support our new results are given.     

一般化凸乘积空间上Fan-Browder型不动点定理和平衡点定理

我们得到了一般化凸乘积空间上 Fan- Browder型不动点定理 ,然后利用上述结果给出 (部分 )极大元素和平衡点的存在定理     

Existence and uniqueness of solutions for the nonlinear impulsive fractional differential equations

In this paper, we investigate existence and uniqueness of solutions for nonlinear impulsive fractional differential equations. By utilizing the well-known fixed point theorems, we obtain some sufficient conditions for the uniqueness and existence of the solutions. At the end of the paper, an example is given to illustrate our main results.     

Fixed point and maximal element theorems with applications to abstract economies and minimax inequalities

In this paper, we establish some fixed point theorems for a family of multivalued maps under mild conditions. By using our fixed point theorems, we derive some maximal element theorems for a particular family of multivalued maps, namely the Φ-condensing multivalued maps. As applications of our results, we prove some general equilibrium existence theorems in the generalized abstract economies with preference correspondences. Further applications of our results are also given to minimax inequalities for a family of functions.     

Nonlinear fractional integro-differential Langevin equation involving two fractional orders with three-point multi-term fractional integral boundary conditions

In this article, we study a nonlinear fractional integro-differential Langevin equation involving two fractional orders with three-point multi-term fractional integral boundary conditions. By using fixed point theorems and Leray-Schauder degree theory, some new existence results are obtained. Two examples illustrate our results.     

Existence of Solutions for Fractional Integro-differential Equations with Impulsive and Integral Conditions

This paper presents the existence of solutions for a class of Cauchy problems with integral condition for impulsive fractional integro-differential equations. Based on definition of solution for impulsive fractional integro- differential equations, the existence theorems of solutions of fractional differ- ential equation are obtained by applying fixed point methods. Finally, three examples are given to demonstrate the feasibility of the obtained results.     

Positive solutions for a high-order semipositone fractional differential equation with integral boundary conditions

In this paper, we consider the existence of positive solutions for a high-order semipositone fractional differential equation with Riemann-Stieltjes integral boundary conditions. By Krasnoselskii-Zabreiko fixed point theorem and some inequalities associated with Green’s function, two new existence theorems are obtained in the case that the nonlinearity f is allowed to grow both superlinearly and sublinearly. Finally, two examples are given to illustrate the main results.     

Fixed point theorems for operators on partial metric spaces

Fixed point theorems for operators of a certain type on partial metric spaces are given. Orbitally continuous operators on partial metric spaces and orbitally complete partial metric spaces are defined, and fixed point theorems for these operators are given.     

On a fractional integral equation of periodic functions involving Weyl-Riesz operator in Banach algebras

In this paper, we study the existence of periodic solutions for a nonlinear integral equation of periodic functions involving Weyl-Riesz fractional integral operator under the mixed generalized Lipschitz, Carathéodory and monotonicity conditions. The fixed point theorems due to Dhage are the main tool in carrying out our proofs.     

Positive solutions for a system of coupled fractional boundary value problems

We investigate the existence and multiplicity of positive solutions for a system of Riemann–Liouville fractional differential equations, subject to multipoint boundary conditions that contain fractional derivatives, by using some theorems from the fixed point index theory.