Nontrivial solutions of non-autonomous dirichlet fractional discrete problems

2020 ◽  
Vol 23 (4) ◽  
pp. 980-995
Author(s):  
Alberto Cabada ◽  
Nikolay Dimitrov
Keyword(s):  
Existence And Uniqueness ◽  
Point Boundary ◽  
Nontrivial Solutions ◽  
Fractional Difference ◽  
Nonlinear Part ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Difference Equation ◽  
Discrete Problems ◽  
Series Of Functions

AbstractIn this paper, we introduce a two-point boundary value problem for a finite fractional difference equation with a perturbation term. By applying spectral theory, an associated Green’s function is constructed as a series of functions and some of its properties are obtained. Under suitable conditions on the nonlinear part of the equation, some existence and uniqueness results are deduced.

scholarly journals EXISTENCE AND UNIQUENESS RESULTS FOR A COUPLED SYSTEM OF HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS WITH MULTI-POINT BOUNDARY CONDITIONS

2020 ◽  
pp. 843
Author(s):  
Mohamed Houas ◽  
Khellaf Ould Melha
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Coupled System ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential

In this paper, we have studied existence and uniqueness of solutions for a coupled system of multi-point boundary value problems for Hadamard fractional differential equations. By applying principle contraction and Shaefer's fixed point theorem new existence results have been obtained.

scholarly journals On Separate Fractional Sum-Difference Equations with n-Point Fractional Sum-Difference Boundary Conditions via Arbitrary Different Fractional Orders

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 471 ◽  
Author(s):  
Saowaluck Chasreechai ◽  
Thanin Sitthiwirattham
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Nonlinear Functions ◽  
Fractional Difference ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Banach Contraction ◽  
Fractional Orders ◽  
The Banach Contraction Principle

In this article, we study the existence and uniqueness results for a separate nonlinear Caputo fractional sum-difference equation with fractional difference boundary conditions by using the Banach contraction principle and the Schauder’s fixed point theorem. Our problem contains two nonlinear functions involving fractional difference and fractional sum. Moreover, our problem contains different orders in n + 1 fractional differences and m + 1 fractional sums. Finally, we present an illustrative example.

scholarly journals GREEN’S FUNCTION AND EXISTENCE OF SOLUTIONS FOR A THIRD-ORDER THREE-POINT BOUNDARY VALUE PROBLEM

2019 ◽  
Vol 24 (2) ◽  
pp. 171-178 ◽  
Author(s):  
Sergey Smirnov
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Point Boundary ◽  
Nonlinear Boundary Value Problems ◽  
Uniqueness Of Solutions ◽  
Third Order ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

The solutions of third-order three-point boundary value problemx′′′+f(t,x) = 0, t∈[a,b],x(a) =x′(a) = 0, x(b) =kx(η),whereη∈(a,b),k∈R,f∈C([a,b]×R,R) andf(t,0)6= 0, are the subject of thisinvestigation. In order to establish existence and uniqueness results for the solutions,attention is focused on applications of the corresponding Green’s function. As anapplication, also one example is given to illustrate the result.Keywords:Green’s function, nonlinear boundary value problems, three-point boundaryconditions, existence and uniqueness of solutions.

Existence of solutions of BVPs for fractional Langevin equations involving Caputo fractional derivatives

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Zohre Kiyamehr ◽  
Hamid Baghani
Keyword(s):  
Fixed Point ◽  
Continuous Function ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Existence Of Solutions ◽  
Langevin Equations ◽  
Point Boundary ◽  
Caputo Fractional Derivatives ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

AbstractThis article investigates a nonlinear fractional Caputo–Langevin equationD^{\beta}(D^{\alpha}+\lambda)x(t)=f(t,x(t)),\quad 0<t<1,\,0<\alpha\leq 1,\,1<% \beta\leq 2,subject to the multi-point boundary conditionsx(0)=0,\qquad\mathcal{D}^{2\alpha}x(1)+\lambda\mathcal{D^{\alpha}}x(1)=0,% \qquad x(1)=\int_{0}^{\eta}x(\tau)\,d\tau\quad\text{for some }0<\eta<1,where {D^{\alpha}} is the Caputo fractional derivative of order α, {f:[0,1]\times\mathbb{R}\to\mathbb{R}} is a given continuous function, and λ is a real number. Some new existence and uniqueness results are obtained by applying an interesting fixed point theorem.

Two-point boundary value problems for the generalized Bagley-Torvik fractional differential equation

2013 ◽  
Vol 11 (3) ◽  
Author(s):  
Svatoslav Staněk
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Existence Results ◽  
Point Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Carathéodory Function ◽  
Fractional Differential

AbstractWe investigate the fractional differential equation u″ + A c D α u = f(t, u, c D μ u, u′) subject to the boundary conditions u′(0) = 0, u(T)+au′(T) = 0. Here α ∈ (1, 2), µ ∈ (0, 1), f is a Carathéodory function and c D is the Caputo fractional derivative. Existence and uniqueness results for the problem are given. The existence results are proved by the nonlinear Leray-Schauder alternative. We discuss the existence of positive and negative solutions to the problem and properties of their derivatives.

Three-point fractional h-sum boundary value problems for sequential Caputo fractional h-sum-difference equations

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5727-5742
Author(s):  
Jarunee Soontharanon ◽  
Jiraporn Reunsumrit ◽  
Thanin Sitthiwirattham
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equation ◽  
Existence And Uniqueness ◽  
Difference Operators ◽  
Fractional Difference ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In this article, we study an existence and uniqueness results for a sequential nonlinear Caputo fractional h-sum-difference equation with three-point fractional h-sum boundary conditions, by using the Banach contraction principle and the Schauder?s fixed point theorem. Our problem contains different orders in three fractional difference operators and three fractional sums. Finally, we provide an example to displays the importance of these results.

Sign in / Sign up

Export Citation Format

Share Document