Existence of solutions of infinite system of nonlinear sequential fractional differential equations

Abstract

Abstract In a recent paper (Filomat 32:4577–4586, 2018) the authors have investigated the existence and uniqueness of a solution for a nonlinear sequential fractional differential equation. To present an analytical improvement for Fazli–Nieto’s results with some conditions removed based on a new technique is the main objective of this paper. In addition, we introduce an infinite system of nonlinear sequential fractional differential equations and discuss the existence of a solution for them in the classical Banach sequence spaces c 0 $c_{0}$ and ℓ p $\ell_{p}$ by applying the Darbo fixed point theorem. Moreover, the proposed method is applied to several examples to show the clarity and effectiveness.

Keywords

• Fixed point
• Sequential fractional differential equation
• The Banach fixed point theorem
• Measure of noncompactness
• Infinite system