Boundary value problem for nonlinear fractional differential equations involving Erdélyi-Kober derivative on unbounded domain

In this paper, we establish sufficient conditions for the existence of bounded solution a class boundary value problem nonlinear fractional differential equations involving Erdélyi-Kober operator on unbounded domain. Our results are based fixed point theorem Schauder combined with diagonalization argument method in special Banach space. To that end, an example is presented to illustrate usefulness our main results.