Approximate Controllability of Sub-Diffusion Equation with Impulsive Condition

Abstract

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.

An efficient numerical scheme and its analysis for the multiterm time‐fractional convection‐diffusion‐reaction equation

“…In recent years, fractional calculus (FC) has gained wide attention among researchers due to its long history and growing use in various applications in applied sciences and engineering. Some of the areas of applications of FC include viscoelasticity, continuum mechanics, material science, signal processing, nuclear science, financial markets and electrical network, see in previous works [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16].…”

On the Integral Transform Shehu for Nonlinear Fractional Problems

“…In the modeling of various processes in mathematics, biology, physics, engineering, and so on [9,13,15,16,3,4,10,5], FPDEs are utilized since the results of fractional mathematical models have better results than other mathematical models. Therefore quite a few research, such as the existence, uniqueness, and regularity of solutions, on the processes of heat diusion, modeled by FPDEs [18,11,17]. The contribution of fractional dierential equations plays a vital role in science and technology.…”

Numerical simulation of 3-D fractional-order convection-diffusion PDE by a local meshless method

“…Fractional differential equations contain derivatives of any complex or real order, being considered as general form of differential equations. The comprehensive applications in real world problems are described by fractional PDE and it is found to be an effective tool in interpretation and modeling of numerous problems appear in physics and applied mathematics [3][4][5][6][7][8].…”