Existence of a weak solution for a nonlinear parabolic problem with fractional derivates

Volume 30, Issue 3, pp 226--254 https://doi.org/10.22436/jmcs.030.03.04

Publication Date: January 12, 2023 Submission Date: May 31, 2022 Revision Date: September 22, 2022 Accteptance Date: December 19, 2022

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Authors

R. A. Sanchez-Ancajima - Dept. Mathematics Statistics and Informatics, Universidad Nacional de Tumbes, Peru. L. J. Caucha - Dept. Mathematics Statistics and Informatics, Universidad Nacional de Tumbes, Peru.

Abstract

The primary objective of this study was to demonstrate the existence and uniqueness of a weak solution for a nonlinear parabolic problem with fractional derivatives for the spatial and temporal variables on a one-dimensional domain. Using the Nehari manifold method and its relationship with the Fibering maps, the existence of a weak solution for the stationary case was demonstrated. Finally, using the Arzela-Ascoli theorem and Banach's fixed point theorem, the existence and uniqueness of a weak solution for the nonlinear parabolic problem were shown.

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Keywords

• Fractional calculus
• Nehari manifold
• Fibering maps
• weak Solution

MSC

•  26A33
•  35J20
•  35A05

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