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

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