α-Analytic solutions of some linear fractional differential equations with variable coefficients

This paper investigates the solutions, around an ordinary point x0 ∈ [a, b] for fractional linear differential equations of the form:[Lnα(y)](x)=g(x,α),[Lnα(y)](x)=g(x,α), where[Lnα(y)](x)=y(nα)(x)+∑k=0n-1ak(x)y(kα)(x)with α ∈ (0, 1]. Here n ∈ N, the real functions g(x) and ak(x) (k = 0, 1, … , n − 1) are defined on the interval [a, b], and y(nα)(x) represents sequential fractional derivatives of order kα of the function y(x). This study is an extension of the corresponding works by Al-Bassam.