Fractal Fract, Vol. 7, Pages 417: A Time-Fractional Schrödinger Equation with Singular Potentials on the Boundary

Fractal Fract, Vol. 7, Pages 417: A Time-Fractional Schrödinger Equation with Singular Potentials on the Boundary

Fractal and Fractional doi: 10.3390/fractalfract7060417

Authors: Ibtehal Alazman Mohamed Jleli Bessem Samet

A Schrödinger equation with a time-fractional derivative, posed in (0,∞)×I, where I=]a,b], is investigated in this paper. The equation involves a singular Hardy potential of the form λ(x−a)2, where the parameter λ belongs to a certain range, and a nonlinearity of the form μ(x−a)−ρ|u|p, where ρ≥0. Using some a priori estimates, necessary conditions for the existence of weak solutions are obtained.