The sufficient conditions are derived for the existence of denumerably many positive solutions for fractional order boundary value problem
where denote fractional derivatives of Riemann-Liouville type with denotes Riemann-Liouville fractional integral, is an increasing homeomorphism and positive homomorphism operator(IHPHO), by applying Hölder’s inequality and Krasnoselskii’s cone fixed point theorem in a Banach space.