- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 7 Issue: 1
- On Caputo fractional elliptic equation with nonlocal condition
On Caputo fractional elliptic equation with nonlocal condition
Authors : Tien Nguyen
Pages : 205-214
Doi:10.31197/atnaa.1197560
View : 72 | Download : 143
Publication Date : 2023-03-31
Article Type : Research Article
Abstract :This paper is first study for considering nonlocal elliptic equation with Caputo derivative. We obtain the upper bound of the mild solution. The second contribution is to provide the lower bound of the solution at terminal time. We prove the non-correction of the problem in the sense of Hadamard. The main tool is the use of upper and lower bounds of the Mittag-Lefler function, combined with analysis in Hilbert scales space.Keywords : Fractional evolution equation, Caputo derivative, Mittag-Lefler functions