Existence of solutions to a nonlinear fractional diffusion equation with exponential growth - He, Jia Wei; Zhou, Yong; Alsaedi, Ahmed; Ahmad, Bashir (Nonlinear Analysis: Modelling and Control, 2024)
In this paper, we study a Cauchy problem for a space–time fractional diffusion equation with exponential nonlinearity. Based on the standard Lp-Lq estimates of strongly continuous semigroup generated by fractional Laplace operator, we investigate the existence of global solutions for initial data with small norm in Orlicz space exp Lp(Rd) and a time weighted Lr(Rd) space. In the framework of the Hölder interpolation inequality, we also discuss the existence of local solutions without the Orlicz space.
Keywords: diffusion equation; Caputo’s fractional derivative; exponential growth; Orlicz spaces