Monotone Iterative Technique for Nonlinear Periodic Time Fractional Parabolic Problems

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Original research article

Author(s):

Abdelouahed Alla Hamou^a, Elhoussine Azroul^a, Abdelilah Lamrani Alaoui^b

^aDepartment of Mathematics, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, B.P. 1796, Atlas 30000, Fez, Morocco
^bDepartment of Mathematics, Regional Center of Education and Professional Training, B.P. 49, 30000, Fez, Morocco

Advances in the Theory of Nonlinear Analysis and its Applications 4 (3), 194-213.

Received: July 25, 2020

Accepted: September 5, 2020

Published: September 14, 2020

Abstract

In this paper, existence and uniqueness of weak solutions for a linear parabolic problem with conformable derivative are proved. The existence of weak periodic solutions for conformable fractional parabolic nonlinear differential equations is shown using a more generalized monotone iterative method combined with the method of upper and lower solutions. We also prove the convergence of the monotone sequence to weak periodic minimal and maximal solutions. Moreover, the conformable versions of the Lions–Magness and Aubin–Lions lemmas are established.

Keywords: Nonlinear equation, parabolic equations, conformable fractional derivative, upper and lower solutions, monotone iterative method, conformable Aubin–Lions lemma.

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APA Style

Alaouı, A. L., Azroul, E., & Hamou, A. A. (2020). Monotone iterative technique for nonlinear periodic time fractional parabolic problems. Advances in the Theory of Nonlinear Analysis and its Application , 4 (3), 194-213.