scholarly journals Existence of solutions for a fractional-order boundary value problem

2020 ◽  
Vol 72 (12) ◽  
pp. 1651-1662
Author(s):  
I. Y. Karaca ◽  
D. Oz
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Fractional Order ◽  
Existence Of Solutions ◽  
Boundary Value

UDC 517.9 We investigate the existence of solutions for a fractional-order boundary-value problem by using some fixed point theorems.As applications, examples are given to illustrate the main results.

L 1-solutions of the boundary value problem for implicit fractional order differential equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Benoumran Telli ◽  
Mohammed Said Souid
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Order ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Abstract The aim of this paper is to present new results on the existence of solutions for a class of the boundary value problem for fractional order implicit differential equations involving the Caputo fractional derivative. Our results are based on Schauder’s fixed point theorem and the Banach contraction principle fixed point theorem.

scholarly journals Existence of three positive solutions for boundary value problem with fractional order and infinite delay

2015 ◽  
Vol 53 (1) ◽  
pp. 57-76
Author(s):  
Hedia Benaouda
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fractional Order ◽  
Point Theorem ◽  
Infinite Delay ◽  
Boundary Value

Abstract In this paper we investigate the existence three positives solutions by using Leggett-Williams fixed point theorem in cones for three boundary value problem with fractional order and infinite delay.

scholarly journals Existence of Positive Solution for the Eighth-Order Boundary Value Problem Using Classical Version of Leray–Schauder Alternative Fixed Point Theorem

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 129 ◽  
Author(s):  
Thenmozhi Shanmugam ◽  
Marudai Muthiah ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Eighth Order ◽  
Classical Version ◽  
Nonlinear Alternative

In this work, we investigate the existence of solutions for the particular type of the eighth-order boundary value problem. We prove our results using classical version of Leray–Schauder nonlinear alternative fixed point theorem. Also we produce a few examples to illustrate our 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.

Existence of positive solutions for Riemann–Liouville fractional order three-point boundary value problem

2015 ◽  
Vol 08 (04) ◽  
pp. 1550057 ◽  
Author(s):  
Sabbavarapu Nageswara Rao
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fractional Order ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Point Boundary ◽  
Existence Of Positive Solutions

In this paper, we study the following fractional order three-point boundary value problem [Formula: see text] where [Formula: see text], are the standard Riemann–Liouville fractional order derivatives with [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]: [Formula: see text] is continuous. By using several well-known fixed-point theorems in a cone, the existence of at least one and two positive solutions is obtained. Some examples are presented to illustrate the main results.

scholarly journals Existence Results of a Nonlocal Fractional Symmetric Hahn Integrodifference Boundary Value Problem

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2174
Author(s):  
Rujira Ouncharoen ◽  
Nichaphat Patanarapeelert ◽  
Thanin Sitthiwirattham
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Fixed Point Problem ◽  
Existence Results ◽  
Difference Operators ◽  
Point Problem ◽  
Point Operator

The existence of solutions of nonlocal fractional symmetric Hahn integrodifference boundary value problem is studied. We propose a problem of five fractional symmetric Hahn difference operators and three fractional symmetric Hahn integrals of different orders. We first convert our nonlinear problem into a fixed point problem by considering a linear variant of the problem. When the fixed point operator is available, Banach and Schauder’s fixed point theorems are used to prove the existence results of our problem. Some properties of (q,ω)-integral are also presented in this paper as a tool for our calculations. Finally, an example is also constructed to illustrate the main results.

scholarly journals Existence of Solutions for Integrodifferential Equations of Fractional Order with Antiperiodic Boundary Conditions

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Ahmed Alsaedi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Fractional Order ◽  
Contraction Mapping ◽  
Existence Of Solutions ◽  
Contraction Mapping Principle ◽  
Integrodifferential Equations ◽  
Krasnoselskii’S Fixed Point Theorem

We discuss the existence of solutions for a nonlinear antiperiodic boundary value problem of integrodifferential equations of fractional orderq∈(1,2]. The contraction mapping principle and Krasnoselskii's fixed point theorem are applied to establish the results.

scholarly journals Existence of Solutions for Fractional Integro-Differential Equation with Multipoint Boundary Value Problem in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Yulin Zhao ◽  
Li Huang ◽  
Xuebin Wang ◽  
Xianyang Zhu
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Fixed Point ◽  
Boundary Value Problem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Point Boundary ◽  
Integro Differential Equation ◽  
The Fixed Point Theorem ◽  
Multipoint Boundary Value Problem

By means of the fixed-point theorem in the cone of strict-set-contraction operators, we consider the existence of a nonlinear multi-point boundary value problem of fractional integro-differential equation in a Banach space. In addition, an example to illustrate the main results is given.

scholarly journals L1-Solutions of Boundary Value Problems for Implicit Fractional Order Differential Equations with Integral Conditions

2018 ◽  
Vol 11 ◽  
pp. 8-17
Author(s):  
Mohammed Said Souid
Keyword(s):  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Integral Conditions ◽  
Fractional Order Differential Equations ◽  
Banach Contraction ◽  
The Banach Contraction Principle

The aim of this paper is to present new results on the existence of solutions for a class of boundary value problem for fractional order implicit di erential equations with integral conditions involving the Caputo fractional derivative. Our results are based on Schauder's xed point theorem and the Banach contraction principle fi xed point theorem.

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