On a time fractional diffusion equation with nonlocal initial conditions
Abstract
The paper examines the existence and regularity of solutions for fractional diffusion equation with nonlocal initial condition. {After constructing a mild formulation for the solution, several existence and regularity results are investigated in two distinct spaces including $L^p$ and $L^\infty$}. Using some techniques of Fourier series and Parseval's equality, we show the well-posedness result of our problem. Finally, we show that the convergence results of the mild solution when two parameters $\ep, \beta $ tends to zero. {The solution of the present problem is shown to converge to the solution of the initial value problem as the parameter $\beta$ tends to zero.
Published
2021-08-24
Section
Articles