scholarly journals Sufficient conditions for the existence of solutions for boundary value problems for fractional differential equations

2020 ◽  
Author(s):  
Abdulkadir Dogan
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Fractional Differential ◽  
Set Up

In this article, we set up adequate circumstances for the existence of solutions for boundary value problems of fractional differential equations including the Caputo fractional derivative and nonlocal conditions.

Boundary Value Problems for Fractional Differential Equations

2009 ◽  
Vol 16 (3) ◽  
pp. 401-411 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Mouffak Benchohra ◽  
Samira Hamani
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Caputo Fractional Derivative ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Fractional Differential

Abstract The sufficient conditions are established for the existence of solutions for a class of boundary value problems for fractional differential equations involving the Caputo fractional derivative.

A new method for converting boundary value problems for impulsive fractional differential equations to integral equations and its applications

2017 ◽  
Vol 8 (1) ◽  
pp. 386-454 ◽  
Author(s):  
Yuji Liu
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Periodic Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Impulsive Fractional Differential Equations ◽  
Periodic Boundary Value Problems ◽  
Fractional Differential

Abstract In this paper, we present a new method for converting boundary value problems of impulsive fractional differential equations to integral equations. Applications of this method are given to solve some types of anti-periodic boundary value problems for impulsive fractional differential equations. Firstly by using iterative method, we prove existence and uniqueness of solutions of Cauchy problems of differential equations involving Caputo fractional derivative, Riemann–Liouville and Hadamard fractional derivatives with order {q\in(0,1)} , see Theorem 2, Theorem 4, Theorem 6 and Theorem 8. Then we obtain exact expression of piecewise continuous solutions of these fractional differential equations see Theorem 1, Theorem 2, Theorem 3 and Theorem 4. Finally, four classes of integral type anti-periodic boundary value problems of singular fractional differential equations with impulse effects are proposed. Sufficient conditions are given for the existence of solutions of these problems. See Theorems 4.1–4.4. We allow the nonlinearity {p(t)f(t,x)} in fractional differential equations to be singular at {t=0,1} and be involved a super-linear and sub-linear term. The analysis relies on Schaefer’s fixed point theorem. In order to avoid misleading readers, we correct the results in [28] and [65]. We establish sufficient conditions for the existence of solutions of an anti-periodic boundary value problem for impulsive fractional differential equation. The results in [68] are complemented. The results in [81] are corrected. See Lemma 5.1, Lemma 5.7, Lemma 5.10 and Lemma 5.13.

scholarly journals Existence of Positive Solutions for Two-Point Boundary Value Problems of Nonlinear Finite Discrete Fractional Differential Equations and Its Application

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Caixia Guo ◽  
Jianmin Guo ◽  
Ying Gao ◽  
Shugui Kang
Keyword(s):  
Green Function ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Point Boundary ◽  
Fractional Differential ◽  
The Green Function

This paper is concerned with the two-point boundary value problems of nonlinear finite discrete fractional differential equations. On one hand, we discuss some new properties of the Green function. On the other hand, by using the main properties of Green function and the Krasnoselskii fixed point theorem on cones, some sufficient conditions for the existence of at least one or two positive solutions for the boundary value problem are established.

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