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.

Two point fractional boundary value problems with a fractional boundary condition

2018 ◽  
Vol 21 (2) ◽  
pp. 442-461 ◽  
Author(s):  
Jeffrey W. Lyons ◽  
Jeffrey T. Neugebauer
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence Of Positive Solutions ◽  
Fractional Boundary Conditions ◽  
Fractional Boundary Value Problems

Abstract In this paper, we employ Krasnoseľskii’s fixed point theorem to show the existence of positive solutions to three different two point fractional boundary value problems with fractional boundary conditions. Also, nonexistence results are given.

scholarly journals Blow-Up Solutions for a Singular Nonlinear Hadamard Fractional Boundary Value Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Imed Bachar ◽  
Said Mesloub
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Blow Up ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Fractional Boundary Value Problems

We consider singular nonlinear Hadamard fractional boundary value problems. Using properties of Green’s function and a fixed point theorem, we show that the problem has positive solutions which blow up. Finally, some examples are provided to explain the applications of the results.

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 Further results on existence of positive solutions of generalized fractional boundary value problems

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hojjat Afshari ◽  
Mohammed S. Abdo ◽  
Jehad Alzabut
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Fractional Operators ◽  
New Approach ◽  
Existence Of Positive Solutions ◽  
Contractive Type ◽  
Fractional Boundary Value Problems

Abstract This paper studies two classes of boundary value problems within the generalized Caputo fractional operators. By applying the fixed point result of α-ϕ-Geraghty contractive type mappings, we derive new results on the existence and uniqueness of the proposed problems. Illustrative examples are constructed to demonstrate the advantage of our results. The theorems reported not only provide a new approach but also generalize existing results in the literature.

Existence of solutions for Caputo fractional boundary value problems with integral conditions

2017 ◽  
Vol 33 (2) ◽  
pp. 207-217
Author(s):  
WENJUN LIU ◽  
◽  
HEFENG ZHUANG ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Point Theorem ◽  
Boundary Value ◽  
Integral Conditions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Nonlinear Alternative ◽  
Banach’S Contraction Principle ◽  
Fractional Boundary Value Problems

In this paper, we investigate the existence results for Caputo fractional boundary value problems with integral conditions. Our analysis relies on Banach’s contraction principle, Leray-Schauder nonlinear alternative, Boyed and Wong fixed point theorem, and Krasnoselskii’s fixed point theorem. As applications, some examples are provided to illustrate our main results.

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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