A nondivergence parabolic problem with a fractional time derivative. (English) Zbl 1449.35428

Allen, Mark

Differ. Integral Equ. 31, No. 3-4, 215-230 (2018).

The author considers a nonlocal nonlinear parabolic problem with a fractional time derivative. A Krylov-Safonov type result is proved. In particular, a Hölder regularity of solutions is shown. The estimates given in the article remain uniform as the order of the fractional time derivative \(\alpha\to 1\).

Reviewer: Abdallah Bradji (Annaba)

MSC:

35R11	Fractional partial differential equations
35K55	Nonlinear parabolic equations

Keywords:

nondivergence parabolic equation; fractional time derivative