On fractional modelling of dye removal using fractional derivative with non-singular kernel

RETRACTED: Optimal control of fractional order singular system

“…In last few decades many researchers from different fields showed their interest on fractional calculus because the systems described using fractional differential equations give more realistic behaviour. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] Fractional calculus deals with the differentiation and integration of arbitrary real order. It plays a significant role in almost…”

New aspects on the fractional Euler-Lagrange equation with non-singular kernels

“…It is believed to be powerful in describing nonlinear phenomena since one can access a heterogeneity of the system through the given fractional order. To elaborate on the novelty of this fractional calculus topic, we refer to some of the following papers, and the references therein, to the readers [1][2][3][4][5][6][7][8][9][10]. In the past years, studying the dynamics of some physical system, through Lagrange's or Hamilton's equation by generalizing it to the fractional case, intrigued many scientists because of its capability in describing some fractional dimensions.…”

Separation and stability of solutions to nonlinear systems involving Caputo–Fabrizio derivatives

“…The well-posedness for the differential systems with the CFFD was well investigated in the published studies [35][36][37][38][39][40][41][42]; among them, the existence of solutions for a coupled system of differential inclusions was discussed in [37] by using some fixed point theorems for the multivalued maps, the existence of solutions and of approximate solutions for some high-order fractional integrodifferential equations were completely considered in [38] and [39][40][41], respectively, by means of fixed point theorems and by virtue of approaches involving α-contractive maps, and the results for the existence and dimension of the set of solutions were obtained in [42] for the second fractional integro-differential inclusion problem with the extended CFFD. And more importantly, the differential equations involving the CFFD have found a wide range of applications [43][44][45][46][47][48][49].…”