Local existence theorem of fractional differential equations in Lp space

الملخص EN

We proved the existence of P-integrable solution in Lp (a,b) -space, where 1 p   for the fractional differential equation which has the form: cD y(t)  f (t, y(t)) 0  1 with boundary condition  y (a)  y (b )  c where D is the Caputo fractional derivative,  , and c are positive constants with    0 .

The contraction mapping principle has been used to establish our main result.