Here we define a Caputo like discrete nabla fractional difference and we produce discrete nabla fractional Taylor formulae for the first time. We estimate their remaiders. Then we derive related discrete nabla fractional Opial, Ostrowski, Poincaré and Sobolev type inequalities .

In the paper under review, we analyze a class of abstract distributionally chaotic (multi-term) fractional differential equations in Banach spaces, associated with use of the Caputo fractional derivatives. AMS Mathematics Subject Classification (2010): 47A16, 47D03, 47D06, 47D99

Copyright 2011 by [Vincenzina Caputo, Maria Carmela Aprile, Rodolfo M. Nayga Jr.]. All rights reserved. Readers may make verbatim copies of this document for non commercial purposes by any means, provided that this copyright notice appears on all such copies.

Previously, based on the method of (radial powers) radial basis functions, we proposed a procedure for approximating derivative values from one-dimensional scattered noisy data. In this work, we show that the same approach also allows us to approximate the values of (Caputo) fractional derivatives (for orders between 0 and 1). With either an a priori or a posteriori strategy of choosing the reg...

This survey paper is concerned with some of the most recent results on Lyapunov-type inequalities for fractional boundary value problems involving a variety derivative operators and conditions. Our work deals Caputo, Riemann-Liouville, ?-Caputo, ?-Hilfer, hybrid, Caputo-Fabrizio, Hadamard, Katugampola, Hilfer-Katugampola, p-Laplacian, proportional operators.

In this paper, we investigate numerical approximations of the scalar conservation law with the Caputo derivative, which introduces the memory effect. We construct the first order and the second order explicit upwind schemes for such equations, which are shown to be conditionally 1 contracting and TVD. However, the Caputo derivative leads to the modified CFL-type stability condition, ( t) = O( x...

*Correspondence: [email protected] Department of Mathematics and Physical Sciences, Prince Sultan University, P.O. Box 66833, Riyadh, 11586, Saudi Arabia Abstract In this article, we extend fractional calculus with nonsingular exponential kernels, initiated recently by Caputo and Fabrizio, to higher order. The extension is given to both left and right fractional derivatives and integrals. ...

Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th anniversary In the paper, maximum principle for the generalized time-fractional diffusion equations including the multi-term diffusion equation and the diffusion equation of distributed order is formulated and discussed. In these equations, the time-fractional derivative is defined in the Caputo sense. In contrast to the Riemann...