Existence of Positive Solutions for a Coupled System of (p, q)-Laplacian Fractional Higher Order Boundary Value Problems (original) (raw)

Existence of Positive Solutions to a Family of Fractional Two Point Boundary Value Problems

Progress in Fractional Differentiation and Applications, 2016

In this paper we will consider an nth order fractional boundary value problem with boundary conditions that include a fractional derivative at 1. We will develop properties of the Green's Function for this boundary value problem and use these properties along with the Contraction Mapping Principle, and the Schuader's, Krasnozel'skii's, and Legget-Williams fixed point theorems to prove the existence of positive solutions under different conditions. v

Existence of positive solutions for p-Laplacian boundary value problems of fractional differential equations

Boundary Value Problems, 2022

In this paper, we study the existence and multiplicity of ρ-concave positive solutions for a p-Laplacian boundary value problem of two-sided fractional differential equations involving generalized-Caputo fractional derivatives. Using Guo-Krasnoselskii fixed point theorem and under some additional assumptions, we prove some important results and obtain the existence of at least three solutions. To establish the results, Green functions are used to transform the considered two-sided generalized Katugampola and Caputo fractional derivatives. Finally, applications with illustrative examples are presented to show the validity and correctness of the obtained results.

Existence of triple positive solutions for boundary value problem of nonlinear fractional differential equations

Computational Methods for Differential Equations, 2017

This article is devoted to the study of existence and multiplicity of positive solutions to a class of nonlinear fractional order multi-point boundary value problems of the type−Dq0+u(t) = f(t, u(t)), 1 < q ≤ 2, 0 < t < 1,u(0) = 0, u(1) =m−2∑ i=1δiu(ηi),where Dq0+ represents standard Riemann-Liouville fractional derivative, δi, ηi ∈ (0, 1) withm−2∑i=1δiηi q−1 < 1, and f : [0, 1] × [0, ∞) → [0, ∞) is a continuous function. We use some classical results of fixed point theory to obtain sufficient conditions for the existence and multiplicity results of positive solutions to the problem under consideration. In order to show the applicability of our results, we provide some examples.

Existence and Uniqueness of Positive Solutions for Coupled Systems of Fractional ∆-Difference Boundary Value Problems

2016

In this paper, we establish the solvability of coupled systems of two-point fractional ∆-difference boundary value problems. To this aim we use the nonlinear alternative of Leray-Schauder and Krasnoselskii-Zabreiko fixed point theorems for existence results and by imposing Lipschitzian conditions on nonlinearities uniqueness of solutions will be concluded. In this paper, Green functions play crucial role for linking considered fractional ∆-difference boundary value problems and fixed point techniques in relevant Banach spaces. At the end we present some numerical examples to illustrate the obtained main results.

On the existence of nonnegative solutions for a class of fractional boundary value problems

2013

‎In this paper‎, ‎we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation‎. ‎By applying Kranoselskii`s fixed--point theorem in a cone‎, ‎first we prove the existence of solutions of an auxiliary BVP formulated by truncating the response function‎. ‎Then the Arzela--Ascoli theorem is used to take C1C^1C1 limits of sequences of such solutions.

Existence of positive solutions for fractional boundary value problems

Journal of Applied Analysis and Computation, 2017

In this paper, by introducing a new operator, improving and generating a p-Laplace operator for some p > 1, we discuss the existence and multiplicity of positive solutions to the four point boundary value problems of nonlinear fractional differential equations. Our results extend some recent works in the literature.