Parabolic problem with fractional time derivative with nonlocal and nonsingular Mittag-Leffler kernel

Jean Daniel Djida; Juan J. Nieto; Iván Area

doi:10.3934/dcdss.2020033

Article Contents

2020, Volume 13, Issue 3: 609-627. Doi: 10.3934/dcdss.2020033

This issue Previous Article Memorized relaxation with singular and non-singular memory kernels for basic relaxation of dielectric vis-à-vis Curie-von Schweidler & Kohlrausch relaxation laws Next Article Multi-directional and saturated chaotic attractors with many scrolls for fractional dynamical systems

Parabolic problem with fractional time derivative with nonlocal and nonsingular Mittag-Leffler kernel

1.
Departamento de Estatística, Análise Matemática e Optimización, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
2.
African Institute for Mathematical Sciences (AIMS), P.O. Box 608, Limbe Crystal Gardens, South West Region, Cameroon
3.
Departamento de Matemática Aplicada Ⅱ, E.E. Aeronáutica e do Espazo, Universidade de Vigo, Campus As Lagoas s/n, 32004 Ourense, Spain

^* Corresponding author: Iván Area
^* Corresponding author: Iván Area

Received: March 31, 2018

Revised: April 30, 2018

Published: December 2019

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Abstract

We prove Hölder regularity results for nonlinear parabolic problem with fractional-time derivative with nonlocal and Mittag-Leffler nonsingular kernel. Existence of weak solutions via approximating solutions is proved. Moreover, Hölder continuity of viscosity solutions is obtained.

Keywords:

Fractional derivative with Mittag-Leffler function,
Hölder continuity,
nonlocal diffusion,
viscosity solution.

Mathematics Subject Classification: 35K55, 26A33, 35D30.

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References

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