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March  2020, 13(3): 609-627. doi: 10.3934/dcdss.2020033

## 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

Received  April 2018 Revised  May 2018 Published  March 2019

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.

Citation: Jean Daniel Djida, Juan J. Nieto, Iván Area. Parabolic problem with fractional time derivative with nonlocal and nonsingular Mittag-Leffler kernel. Discrete & Continuous Dynamical Systems - S, 2020, 13 (3) : 609-627. doi: 10.3934/dcdss.2020033
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##### References:
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