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.
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.
R. A. Sanchez-Ancajima, L. J. Caucha, Existence of a weak solution for a nonlinear parabolic problem with fractional derivates, Journal of Mathematics and Computer Science, 30 (2023), no. 3, 226--254
Sanchez-Ancajima R. A., Caucha L. J., Existence of a weak solution for a nonlinear parabolic problem with fractional derivates. J Math Comput SCI-JM. (2023); 30(3):226--254
Sanchez-Ancajima, R. A., Caucha, L. J.. "Existence of a weak solution for a nonlinear parabolic problem with fractional derivates." Journal of Mathematics and Computer Science, 30, no. 3 (2023): 226--254
