Boundary Value Problem for Impulsive Delay Fractional Differential Equations with Several Generalized Proportional Caputo Fractional Derivatives

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.

Existence of solutions of boundary value problems for Caputo fractional differential equations on time scales

‎In this paper‎, ‎we study the boundary-value problem of fractional‎ ‎order dynamic equations on time scales‎, ‎$$‎ ‎^c{Delta}^{alpha}u(t)=f(t,u(t)),;;tin‎ ‎[0,1]_{mathbb{T}^{kappa^{2}}}:=J,;;1

Analysis of Caputo Impulsive Fractional Order Differential Equations with Applications

Existence of triple positive solutions for boundary value problem of nonlinear fractional differential equations

This article is devoted to the study of existence and multiplicity of positive solutions to a class of nonlinear fractional order multi-point boundary value problems of the type−Dq0+u(t) = f(t, u(t)), 1 < q ≤ 2, 0 < t < 1,u(0) = 0, u(1) =m−2∑ i=1δiu(ηi),where Dq0+ represents standard Riemann-Liouville fractional derivative, δi, ηi ∈ (0, 1) withm−2∑i=1δiηi q−1 < 1, and f : [0, 1] × [0, ∞) → [0, ...

Stability of Solutions to Impulsive Caputo Fractional Differential Equations

Stability of the solutions to a nonlinear impulsive Caputo fractional differential equation is studied using Lyapunov like functions. The derivative of piecewise continuous Lyapunov functions among the nonlinear impulsive Caputo differential equation of fractional order is defined. This definition is a natural generalization of the Caputo fractional Dini derivative of a function. Several suffic...