Existence of mild solutions for fractional Schrodinger equations in extended Colombeau algebras

نویسندگان
Melliani, Said ID 1
El Mfadel, Ali ID 2
M'hamed, Elomari ID 3
Bourhim, Fatima Ezzahra ID 4

1 Laboratory of Applied Mathematics Scientific Calculus, Sultan Moulay Slimane University, BP 523, 23000, Beni Mellal, Morocco

2 Laboratory of Applied Mathematics Scientific Calculus, Sultan Moulay Slimane University, BP 523, 23000, Beni Mellal, Morocco

3 Laboratory of Applied Mathematics Scientific Calculus, Sultan Moulay Slimane University, BP 523, 23000, Beni Mellal, Morocco

4 Laboratory of Applied Mathematics Scientific Calculus, Sultan Moulay Slimane University, BP 523, 23000, Beni Mellal, Morocco

doi
10.22075/ijnaa.2022.27296.3553
چکیده

The main crux of this research manuscript is to study the existence and uniqueness of generalized mild solutions for nonlinear Schrodinger equations with singular initial conditions in the extended algebras of generalized functions. The proofs are based on generalized semigroups theory and Gronwall's inequality. As an application, our theoretical results have been illustrated by providing a suitable example.

کلیدواژه‌ها
Extended Colombeau algebra, generalized mild solution, generalized function, Schr\