Approximate Controllability of Sub-Diffusion Equation with Impulsive Condition

In this work, we study an impulsive sub-diffusion equation as a fractional diffusion equation of order α ∈ ( 0 , 1 ) . Existence, uniqueness and regularity of solution of the problem is established via eigenfunction expansion. Moreover, we establish the approximate controllability of the problem by applying a unique continuation property via internal control which acts on a sub-domain.

Existence, Uniqueness and Stability of Nonlinear Implicit Fractional Dynamical Equation with Impulsive condition on Time Scales

The main motive of this research article is to establish the existence, uniqueness and stability results for the non-linear fractional differential equation with impulsive condition on time scales. Banach, Leray-Schauder’s alternative type fixed point theorems are used to examine these results. Further, we give the existence and uniqueness of solution for the corresponding non-local problem. Moreover, to outline the utilization of these outcomes some examples are given.

Kinetic and entropy solutions of quasilinear impulsive hyperbolic equations

In the present paper we deal with kinetic and entropy solutions of quasilinear impulsive hyperbolic equations. The genuine nonlinearity condition enables to prove the existence of one-sided traces of these solutions on fixed-time hyperplanes. The latter fact provides the impulsive condition. This type of equations can be used in the fluctuating hydrodynamics.