Existence theory for boundary value problems for fractional differential equations

In this paper, we investigate the existence of solutions for boundary value problems concerning fractional differential equations in L
^p
(1 ≤ p <; ∞) spaces. Our analysis relies on the Riesz Compactness Criteria and the Leray-Schauder Nonlinear Alternative theorem. Furthermore, we establish an existence principle which guarantees a solution in L
^p
_loc
(1 ≤ p <; ∞), which is a Fréchet space.