Lebesgue measurable function in fractional differential equations

Abstract EN

Bassam, M.A.

[1], proved some existence and uniqueness theorems for the following fractional linear differential equation.

Lna (y) =∑_(i=0)^n▒〖pi 〗 [(n-i) a] (x) = F (x)..1 With the initial conditions Y (k a-1) (a) = U k Where a < x < b, 0 < 1, k are real numbers, k = 1, 2, n, pi (x), F (x) are continuous functions defined on (a, b) such that p0 (x) 0, I = 0, 1, n and y [(n-i)] denotes the fractional derivative of order (n-i) for the function y = In this work we prove some theorems for equation (1), however for =1.

Equation (1) Is an ordinary differential equation o order n, therefore all the theorems proved here will be reduced to well-known result in the theory of ordinary differential equations.

Moreover We give some examples and an application for equation (1).