... 13 06 2012 This paper derives the time-varying initialization function for the Caputo derivative with order between zero and one. The derivative is redefined to include this initialization function. Then, the Laplace transform for the redefined Caputo derivative is determined which...

... WITH CAPUTO DERIVATIVE Changpin Li Department of Mathematics Shanghai University Shanghai 200444, China Email: [email protected] Fengrong Zhang Department of Mathematics Shanghai University Shanghai 200444, China and School of Mathematics and Computational Science China University of Petroleum (East China...

... vector. Numerical simulations applied to Riemann-Liouville and Caputo derivatives demonstrate that the initial conditions problem can be solved thanks to the estimation of the initial state vector of the fractional integrator. Keywords: Riemann-Liouville derivative, Caputo derivative, fractional...

... 14 07 2010 This paper considers the initialization of fractional-order differential equations. The initialization responses obtained using the Caputo derivative are compared with the exact initialization responses from the Riemann-Liouville definition of the fractional derivative...

... initialized Riemann-Liouville fractional integral, and finally the Caputo derivative. Self-consistency was found for the first two cases. The Caputo fractional derivative operator was found to be self-inconsistent based on possible continuation functions derived from the Laplace transform of the derivative...

... fractional order diffusion equation, Caputo derivative, Finite element method, finite element method, error analysis. Address all correspondence to this author INTRODUCTION Fractional calculus can be considered as a generalization of the usual integer-order calculus. It has a history of at least three...