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.

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 Boundary value problems for Caputo-Hadamard fractional differential inclusions with Integral Conditions

2020 ◽  
Vol 6 (1) ◽  
pp. 62-75
Author(s):  
Ahmed Zahed ◽  
Samira Hamani ◽  
Johnny Henderson
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Fractional Differential Inclusions ◽  
Integral Conditions ◽  
Right Hand ◽  
Fractional Differential

AbstractFor r ∈ (1, 2], the authors establish sufficient conditions for the existence of solutions for a class of boundary value problem for rth order Caputo-Hadamard fractional differential inclusions satisfying nonlinear integral conditions. Both cases of convex and nonconvex valued right hand sides are considered.

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.

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 Some Antiperiodic Boundary Value Problem for Nonlinear Fractional Impulsive Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Xianghu Liu ◽  
Yanfang Li
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Existence Of Solutions ◽  
Integral Formula ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Uniqueness Of Solutions ◽  
Liouville Fractional Derivative

This paper is concerned with the sufficient conditions for the existence of solutions for a class of generalized antiperiodic boundary value problem for nonlinear fractional impulsive differential equations involving the Riemann-Liouville fractional derivative. Firstly, we introduce the fractional calculus and give the generalized R-L fractional integral formula of R-L fractional derivative involving impulsive. Secondly, the sufficient condition for the existence and uniqueness of solutions is presented. Finally, we give some examples to illustrate our 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.

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