scholarly journals Application of the fixed point theorems on the existence of solutions for q-fractional boundary value problems

2019 ◽  
Vol 4 (3) ◽  
pp. 997-1018 ◽  
Author(s):  
Sina Etemad ◽  
◽  
Sotiris K. Ntouyas ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Fractional Boundary Value Problems

scholarly journals Solvability of Some Fractional Boundary Value Problems with a Convection Term

2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
Yongfang Wei ◽  
Zhanbing Bai
Keyword(s):  
Fixed Point ◽  
Green Function ◽  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Existence Results ◽  
Convection Term ◽  
Triple Positive Solutions ◽  
Fractional Boundary Value Problems

This paper is devoted to the research of some Caputo’s fractional derivative boundary value problems with a convection term. By the use of some fixed-point theorems and the properties of Green function, the existence results of at least one or triple positive solutions are presented. Finally, two examples are given to illustrate the main results.

scholarly journals The Existence of Solutions to a System of Discrete Fractional Boundary Value Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Yuanyuan Pan ◽  
Zhenlai Han ◽  
Shurong Sun ◽  
Yige Zhao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Continuous Functions ◽  
Fractional Boundary Value Problems ◽  
Schäuder Fixed Point Theorem

We study the existence of solutions for the boundary value problem-Δνy1(t)=f(y1(t+ν-1),y2(t+μ-1)),-Δμy2(t)=g(y1(t+ν-1),y2(t+μ-1)),y1(ν-2)=Δy1(ν+b)=0,y2(μ-2)=Δy2(μ+b)=0, where1<μ,ν≤2,f,g:R×R→Rare continuous functions,b∈N0. The existence of solutions to this problem is established by the Guo-Krasnosel'kii theorem and the Schauder fixed-point theorem, and some examples are given to illustrate the main results.

scholarly journals Some Results on Fractional m-Point Boundary Value Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Huijuan Zhu ◽  
Baozhi Han ◽  
Jun Shen
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Point Boundary ◽  
Lyapunov’S Inequality ◽  
The Given ◽  
Stability Results

In this paper, we will apply some fixed-point theorems to discuss the existence of solutions for fractional m-point boundary value problems D 0 + q u ″ t = h t f u t , t ∈ 0 , 1 , 1 < q ≤ 2 , u ′ 0 = u ″ 0 = u 1 = 0 , u ″ 1 − ∑ i = 1 m − 2 α i u ‴ ξ i = 0 . In addition, we also present Lyapunov’s inequality and Ulam-Hyers stability results for the given m-point boundary value problems.

scholarly journals Applying new fixed point theorems on fractional and ordinary differential equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Erdal Karapınar ◽  
Thabet Abdeljawad ◽  
Fahd Jarad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Existence Of Solution ◽  
Fractional Operators ◽  
Integral Type ◽  
Type Boundary ◽  
Fractional Boundary Value Problems

Abstract In this paper, we consider a fixed point theorem that extends and unifies several existing results in the literature. We apply the proven fixed point results on the existence of solution of ordinary boundary value problems and fractional boundary value problems with integral type boundary conditions in the frame of some Caputo type fractional operators.

scholarly journals On the existence of positive solutions for generalized fractional boundary value problems

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Arjumand Seemab ◽  
Mujeeb Ur Rehman ◽  
Jehad Alzabut ◽  
Abdelouahed Hamdi
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Green Functions ◽  
Fractional Operators ◽  
Existence Of Positive Solutions ◽  
Different Types ◽  
Fractional Boundary Value Problems

AbstractThe existence of positive solutions is established for boundary value problems defined within generalized Riemann–Liouville and Caputo fractional operators. Our approach is based on utilizing the technique of fixed point theorems. For the sake of converting the proposed problems into integral equations, we construct Green functions and study their properties for three different types of boundary value problems. Examples are presented to demonstrate the validity of theoretical findings.

scholarly journals Boundary Value Problems forq-Difference Inclusions

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Nonseparated Boundary Conditions ◽  
Difference Inclusions ◽  
The Right

We investigate the existence of solutions for a class of second-orderq-difference inclusions with nonseparated boundary conditions. By using suitable fixed-point theorems, we study the cases when the right-hand side of the inclusions has convex as well as nonconvex values.

scholarly journals Existence of an approximate solution for a class of fractional multi-point boundary value problems with the derivative term

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yanbin Sang ◽  
Luxuan He
Keyword(s):  
Fixed Point ◽  
Approximate Solution ◽  
Boundary Value Problems ◽  
Unique Solution ◽  
Fixed Point Theorems ◽  
Nonlinear Operator ◽  
Boundary Value ◽  
Point Boundary ◽  
Derivative Term ◽  
Fractional Boundary Value Problems

AbstractIn this paper, we consider a class of fractional boundary value problems with the derivative term and nonlinear operator term. By establishing new mixed monotone fixed point theorems, we prove these problems to have a unique solution, and we construct the corresponding iterative sequences to approximate the unique solution.

scholarly journals Nonlocal Fractional Boundary Value Problems Involving Mixed Right and Left Fractional Derivatives and Integrals

Axioms ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 50 ◽  
Author(s):  
Ahmed Alsaedi ◽  
Abrar Broom ◽  
Sotiris K. Ntouyas ◽  
Bashir Ahmad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Point Theorem ◽  
Fractional Derivatives ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Fractional Integrals ◽  
Derivatives Of ◽  
Fractional Boundary Value Problems

In this paper, we study the existence of solutions for nonlocal single and multi-valued boundary value problems involving right-Caputo and left-Riemann–Liouville fractional derivatives of different orders and right-left Riemann–Liouville fractional integrals. The existence of solutions for the single-valued case relies on Sadovskii’s fixed point theorem. The first existence results for the multi-valued case are proved by applying Bohnenblust-Karlin’s fixed point theorem, while the second one is based on Martelli’s fixed point theorem. We also demonstrate the applications of the obtained results.

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