Analysis of Fractional Differential Equations

Abstract

We discuss existence, uniqueness, and structural stability of solutions of nonlinear differential equations of fractional order. The differential operators are taken in the Riemann-Liouville sense and the initial conditions are specified according to Caputo's suggestion, thus allowing for interpretation in a physically meaningful way. We investigate in particular the dependence of the solution on the order of the differential equation and on the initial condition, and we relate our results to the selection of appropriate numerical schemes for the solution of fractional differential equations.  2002 Elsevier Science

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“…Some fundamental results related to solving fractional differential equations may be found in Miller and Ross [2], Podlubny [3], Kilbas et al [4], Diethelm and Ford [5], and Diethelm [6].…”

Dynamics analysis of fractional order Yu-Wang system

“…A modification of Adams-BashforthMoulton algorithm proposed by Diethelm et al [38][39][40] is used for numerical observations of chaotic trajectories. The system exhibits chaos for α ≥ 0 98.…”

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“…Fractional calculus, as a natural extension of the classical calculus, has the history of more than 300 years [3,4,7,8,9]. In fact, since the beginning of the theory of differential and integral calculus, the mathematicians began their investigations of the calculation of noninteger order derivatives and integrals.…”

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