Monotone Iterative Technique for Nonlinear Periodic Time Fractional Parabolic Problems

Year 2020, Volume: 4 Issue: 3, 194 - 213, 31.08.2020

Abdelilah Lamranı Alaouı , Elhoussine Azroul , Abdelouahed Alla Hamou

https://doi.org/10.31197/atnaa.770669

Cited By: 2

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

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