EXISTENCE FOR PARTIAL DIFFERENTIAL EQUATIONS WITH FRACTIONAL CAUCHY-EULER OPERATOR

We investigate a boundary value problem for partial differential equation with Cauchy-Euler fractional operator $$\begin{aligned} x^{2\alpha }D_{*,x}^{2\alpha } u(x,y)+ x^{\alpha }D_{*,x}^{\alpha u(x,y) + u_{yy}(x,y)=f(x,y),\ 0< x<\infty ,\ 01$$ . However, some cases, solution is found entire semi-infinite strip $$x>0$$ analysis supported by computations, exhibit high level accuracy.