Qualitative theory and approximate solution to a dynamical system under modified type Caputo-Fabrizio derivative

Abstract

<abstract><p>Qualitative theory, together with approximate solutions to a dynamic system, are investigated. The proposed mathematical model is composed of protected, susceptible, infected and treated classes. The adopted model expresses the mechanism of disease due to Typhoid fever. A modified type Caputo-Fabrizio fractional derivative (CFFD) is considered for the intended results. With the help of fixed point theory, some sufficient conditions for the existence of approximate solutions are developed. Also, to compute an approximate solution with respect to each compartment, we utilize the Laplace Transform and the Adomian decomposition method (ADM). A graphical presentation corresponding to some fundamental data is given.</p></abstract>

Numerical solution of a fractional coupled system with the Caputo-Fabrizio fractional derivative

“…In the articles [22][23][24] several methods and issues for solving and modeling solutions to problems in applied mathematics and proofs for important theories were presented. Moreover, the authors investigated the existence and uniqueness results for some coupled systems involving C-F derivatives, for instance see [25][26][27][28][29] and the references cited therein.…”

“…In the third Section, the Picard-Lindelöf technique and the Banach fixed point theorem is applied to obtain uniqueness of solutions for system (1). In the articles [17,29,30], several methods and issues for solving and modeling solutions to problems in applied mathematics and proofs for important theories were presented, and we choose in the fourth Section, the Adomin Decomposition Method (ADM) to construct approximate solutions of the problem (1). A numerical example is given in last Section to illustrate our main results.…”