On initial value problem of random fractional differential equation with impulses

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

On the existence and uniqueness of solution of initial value problem for fractional order differential equations on time scales

n this paper, at first the  concept of Caputo fractionalderivative is generalized on time scales. Then the fractional orderdifferential equations are introduced on time scales. Finally,sufficient and necessary conditions are presented for the existenceand uniqueness of solution of initial valueproblem including fractional order differential equations.

On boundary value problem for fractional differential equations

In this paper‎, ‎we study the existence of solutions for a‎ ‎ fractional boundary value problem‎. ‎By using critical point theory‎ ‎ and variational methods‎, ‎we give some new criteria to guarantee‎ ‎ that‎ ‎ the problems have at least one solution and infinitely many solutions.

Triple Positive Solutions for Boundary Value Problem of a Nonlinear Fractional Differential Equation

Boundary value problem of a nonlinear Langevin equation with two different fractional orders and impulses

*Correspondence: [email protected] 2Department of Mathematics, China University of Petroleum, Qingdao, Shandong 266555, P.R. China Full list of author information is available at the end of the article Abstract In this paper, we study a new type of a Langevin equation involving two different fractional orders and impulses. Sufficient conditions are formulated for the existence and uniqueness ...