New class of n-order fractional differential equations and solvability in the double sequence space m2(∆u v , φ, p)

Source abstract

First, we define a new class of fractional differential equations of order n − 1 ϑ ≤ n, (n ≥ 2). Also, we define a new Banach double sequence space m2(∆u v , φ, p) and a Hausdorff MNC on it. By using this MNC, we prove the existence of solution of infinite system of a new class of fractional differential equations of order ϑ ∈ (n − 1, n], (n ≥ 2) in m2(∆u v , φ, p). Finally, we give two examples to verify the usefulness of our main result.