Existence results for convection-reaction fractional problem involving the distributional Riesz derivative

The main goal of this manuscript is to study the existence results in the Bessel Potential space for the following convection-reaction fractional problem involving by distributional Riesz fractional derivative, {-D-alpha.(D(alpha)u(x)) - div(alpha) (b phi(u(x))) = f(x, u(x), D(alpha)u(x)) in Omega, u = 0 on R-d/Omega, where Omega subset of R-d is a bounded open set with a Lipschitz boundary, alpha is an element of (0, 1) and d > 2 alpha. To reach our goal, we use the application of the Schauder fixed point theory with some assumption on the nonlinear terms phi and f.

Automated summary

The main goal of this manuscript is to study the existence results in the Bessel Potential space for a convection-reaction fractional problem involving distributional Riesz fractional derivative. This study applies the Schauder fixed point theory and makes assumptions on the nonlinear terms to reach the goal of the research.