Journal ArticleDOI
On positive solutions of a nonlocal fractional boundary value problem
Reads0
Chats0
TLDR
In this paper, the existence and uniqueness of positive solutions for a nonlocal boundary value problem of fractional differential equation was investigated, and the uniqueness of the positive solution was obtained by the use of contraction map principle and some Lipschitz type conditions.Abstract:
In this paper, we investigate the existence and uniqueness of positive solutions for a nonlocal boundary value problem of fractional differential equation. Firstly, we give Green’s function and prove its positivity; secondly, the uniqueness of positive solution is obtained by the use of contraction map principle and some Lipschitz-type conditions; thirdly, by means of the fixed point index theory, we obtain some existence results of positive solution. The proofs are based upon the reduction of the problem considered to the equivalent Fredholm integral equation of second kind.read more
Citations
More filters
Journal ArticleDOI
On the concept and existence of solution for impulsive fractional differential equations
TL;DR: In this paper, the existence of a solution for impulsive Cauchy problems with fractional derivative is investigated and sufficient conditions for existence of the solutions are established by applying fixed point methods.
Journal ArticleDOI
Ulam stability and data dependence for fractional differential equations with Caputo derivative
JinRong Wang,Linli Lv,Yong Zhou +2 more
TL;DR: In this paper, Ulam stability and data dependence for fractional differential equations with Caputo fractional derivative of order are studied, and four types of stability results are presented for the case of 0 < � < 1 and b = + 1 by virtue of the Henry-Gronwall inequality.
Journal ArticleDOI
Nonlinear impulsive problems for fractional differential equations and Ulam stability
TL;DR: The concept of piecewise continuous solutions for impulsive Cauchy problems and impulsive boundary value problems respectively are introduced by using a new fixed point theorem and many new existence, uniqueness and data dependence results of solutions are obtained via some generalized singular Gronwall inequalities.
Journal ArticleDOI
Uniqueness of solution for boundary value problems for fractional differential equations
Yujun Cui,Yujun Cui +1 more
TL;DR: This work investigates the uniqueness of solutions for a class of nonlinear boundary value problems for fractional differential equations with Lipschitz constant related to the first eigenvalues corresponding to the relevant operators.
Journal ArticleDOI
Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions
TL;DR: In this article, the boundary value problem of Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions was investigated and new existence results were obtained by applying standard fixed point theorems.
References
More filters
Book
Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
Book
Theory and Applications of Fractional Differential Equations
TL;DR: In this article, the authors present a method for solving Fractional Differential Equations (DFE) using Integral Transform Methods for Explicit Solutions to FractionAL Differentially Equations.
Book
An Introduction to the Fractional Calculus and Fractional Differential Equations
Kenneth S. Miller,Bertram Ross +1 more
TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.