Existence of positive solution for a fractional order nonlinear differential system involving a changing sign perturbation

Abstract

In this paper, we study a class of singular fractional order differential system with a changing-sign perturbation which arises from fluid dynamics, biological models, electrical networks with uncertain physical parameters and parametrical variations in time. Under suitable growth condition, the singular changingsign system is transformed to an approximately singular fractional order differential system with positive nonlinear term, then the existence of positive solution is established by using the known fixed point theorem.

The nonlocal coupled system of Caputo–Fabrizio fractional q‐integro differential equation

“…In recent years, Caputo and Fabrizio introduced a new operator with a nonsingular kernel known as the Caputo-Fabrizio operator [4]. A large number of papers have recently been published dealing with the existence of solutions to nonlinear fractional differential equations using nonlinear analysis techniques [5][6][7][8][9][10][11][12][13]. Also, many researchers used the new definitions of fractional derivative and integral Caputo-Fabrizio to solve several fractional differential equations [14][15][16][17][18][19].…”