Doubly Fractional Nonlinear Parabolic Initial Boundary

In this paper, we introduce a new class of doubly nonlinear parabolic equations, motivated by the ‐Sobolev flow problem and the ‐Hilfer operators in fractional Sobolev space. We discuss some special cases; in particular, when in a bounded domain in Euclidean space, we obtain the fractional Yamabe flow, and when and , we obtain the Yamabe flow. We investigate the existence of a weak solution to these new problems using the Galerkin method and discuss other results throughout the work.