On impulsive partial differential equations with Caputo-Hadamard fractional derivatives

Analysis of Caputo Impulsive Fractional Order Differential Equations with Applications

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...

Existence Theory for Impulsive Partial Hyperbolic Functional Differential Equations Involving the Caputo Fractional Derivative

In this paper we investigate the existence and uniqueness of solutions of a class of partial impulsive hyperbolic differential equations with fixed time impulses involving the Caputo fractional derivative. Our main tool is a fixed point theorem.

On Hadamard and Fej'{e}r-Hadamard inequalities for Caputo $small{k}$-fractional derivatives

In this paper we will prove certain Hadamard and Fejer-Hadamard inequalities for the functions whose nth derivatives are convex by using Caputo k-fractional derivatives. These results have some relationship with inequalities for Caputo fractional derivatives.

Impulsive fractional differential equations with variable times

K e y w o r d s I m p u l s i v e functional differential equations, Variable times, Fixed point. 1. I N T R O D U C T I O N This note is concerned with the existence of solutions, for the initial value problems (IVP for short), for first-order functional differential equations with impulsive effects y' ( t )=f( t , yt), a.e. t e J = [ O , T ] , t¢Tk(y(t)), k = l , . . . , m , (1) y(t +) = Ik(y...