Monotone Iterative Technique for Nonlinear Periodic Time Fractional Parabolic Problems

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Advances in the Theory of Nonlinear Analysis and its Application
Volume: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 : 19 | Download : 7

Publication Date : 2020-08-31

Article Type : Research Paper

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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