Abstract
In this paper, we shall discuss the properties of the well-known Mittag–Leffler function, and consider the existence of solution of the periodic boundary value problem for a fractional differential equation involving a Riemann–Liouville sequential fractional derivative by means of the method of upper and lower solutions and Schauder fixed point theorem.
Highlights
Let J = [a, b] be a compact interval on the real axis R, and y be a measurable Lebesgue function, that is, y ∈ L1(a, b)
We will work here following the definition of a sequential fractional derivative presented by Miller and Ross [3]
There is a close connection between the sequential fractional derivatives and the non sequential Riemann–Liouville derivatives
Summary
We shall consider the existence of solution of the periodic boundary value problem for a fractional differential equation involving a Riemann–Liouville sequential fractional derivative, by using the method of upper and lower solutions and Schauder fixed point theorem. While for the existence of solution of the periodic boundary value problem (1.4) for a fractional differential equation a involving Riemann–Liouville sequential fractional derivative has not been given up to now, the research proceeds slowly and appears some new difficulties in obtaining comparison results. In this paper, we shall discuss the properties of the well-known Mittag–Leffler function, and consider the existence of solution of the periodic boundary value problem (1.4) for a fractional differential equation involving Riemann–Liouville sequential fractional derivative by using the method of upper and lower solutions and Schauder fixed point theorem.
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