A New Numerical Approach for Solving Caputo-Fabrizio Fractional Differential Equations

In this paper, we present a novel numerical scheme for solving fractional-order differential equations of the form ^CFD_t^η ψ ( t ) = f( t,ψ ( t ) ),ψ ( 0 ) = ψ 0,0 < η < 1,t∈[ 0,T ], where ^CFD_t^η denotes the Caputo-Fabrizio derivative operator. Further, we establish the stability and error analysis of the proposed scheme. We also extend this scheme for solving systems of fractional differential equations. Furthermore, we perform the several numerical simulations and present the results graphically. The obtained solutions are compared with those achieved through the well-known methods such as fractional Adams-Bashforth method and a new predictor-corrector method. It has been observed that the proposed method offers greater accuracy than these established methods. Hence, the proposed scheme can be utilized for the simulations of various fractional order differential equations, when the derivatives are considered in the Caputo-Fabrizio sense.