- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 4 Issue: 3
- Monotone Iterative Technique for Nonlinear Periodic Time Fractional Parabolic Problems
Monotone Iterative Technique for Nonlinear Periodic Time Fractional Parabolic Problems
Authors : Abdelilah LAMRANI ALAOUI, Elhoussine AZROUL, Abdelouahed ALLA HAMOU
Pages : 194-213
Doi:10.31197/atnaa.770669
View : 5 | Download : 2
Publication Date : 2020-08-31
Article Type : Research
Abstract :In this paper, the existence and uniqueness of the weak solution for a linear parabolic equation with conformable derivative are proved, the existence of weak periodic solutions for conformable fractional parabolic nonlinear differential equation is proved by using a more generalized monotone iterative method combined with the method of upper and lower solutions. We prove the monotone sequence converge to weak periodic minimal and maximal solutions. Moreover, the conformable version of the Lions-Magness and Aubin–Lions lemmas are also proved.Keywords : Nonlinear equation, parabolic equations, conformable fractional derivative, upper and lower solutions, monotone iterative method, conformable Aubin-Lions lemma