Exponential Euler scheme of multi-delay Caputo-Fabrizio fractional-order differential equations

Abstract This paper establishes the basic structure of the exponential Euler difference form for Caputo–Fabrizio fractional-order differential equations (CF-FODEs) with multiple lags. The research shows that the acquired difference form (i.e., discrete-time CF-FODEs) belongs to the scope of implicit Euler differences and then the fractional PECE algorithm is proposed to solve this implicit difference. At last, global dynamics of the discrete-time CF-FODEs is discussed from the viewpoint of control theory.

[1]  S. Arabia,et al.  Properties of a New Fractional Derivative without Singular Kernel , 2015 .

[2]  J. A. Tenreiro Machado,et al.  A critical analysis of the Caputo-Fabrizio operator , 2018, Commun. Nonlinear Sci. Numer. Simul..

[3]  M. Caputo,et al.  A new Definition of Fractional Derivative without Singular Kernel , 2015 .

[4]  R. T. Matoog,et al.  Study on the mathematical modelling of COVID-19 with Caputo-Fabrizio operator , 2021, Chaos, Solitons & Fractals.

[5]  D. Zorica,et al.  Properties of the Caputo-Fabrizio fractional derivative and its distributional settings , 2018 .

[6]  Delfim F. M. Torres,et al.  Fractional model of COVID-19 applied to Galicia, Spain and Portugal , 2021, Chaos, Solitons & Fractals.

[7]  Juan J. Nieto,et al.  Solution of a fractional logistic ordinary differential equation , 2022, Appl. Math. Lett..

[8]  M. Abbas.  On the initial value problems for the Caputo–Fabrizio impulsive fractional differential equations , 2020 .

[9]  Mireille Bossy,et al.  On the weak convergence rate of an exponential Euler scheme for SDEs governed by coefficients with superlinear growth , 2019 .

[10]  Delfim F. M. Torres,et al.  Solutions of systems with the Caputo–Fabrizio fractional delta derivative on time scales , 2018, Nonlinear Analysis: Hybrid Systems.

[11]  M. Hochbruck,et al.  Exponential Runge--Kutta methods for parabolic problems , 2005 .

[12]  Chengming Huang,et al.  Delay dependent asymptotic mean square stability analysis of the stochastic exponential Euler method , 2021, J. Comput. Appl. Math..

[13]  Jianwen Zhou,et al.  Dynamic behaviours for semi-discrete stochastic Cohen-Grossberg neural networks with time delays , 2020, J. Frankl. Inst..

[14]  I. Khan,et al.  Shape effect on MHD flow of time fractional Ferro-Brinkman type nanofluid with ramped heating , 2021, Scientific Reports.

[15]  Mari Paz Calvo,et al.  A class of explicit multistep exponential integrators for semilinear problems , 2006, Numerische Mathematik.