Here we prove fractional representation formulae involving generalized fractional derivatives, Caputo fractional derivatives and Riemann–Liouville fractional derivatives. Then we establish Poincaré, Sobolev, Hilbert–Pachpatte and Opial type fractional inequalities, involving the right versions of the abovementioned fractional derivatives.

This paper deals with the method of simulation of fractional order chaotic systems. We present a brief survey of the existing fractional order chaotic systems. These systems are described by three fractional differential equations where order of derivatives is a non-integer, arbitrary order. The total order of chaotic system is less than three. We present an approach where we demonstrate by an ...

In this paper, the fractional Sturm-Liouville problems, in which the second order derivative is replaced by a fractional derivative, are derived by the Homotopy perturbation method. The fractional derivatives are described in the Caputo sense. The present results can be implemented on the numerical solutions of the fractional diffusion-wave equations. Numerical results show that HPM is effectiv...

This paper introduces techniques for the estimation of solutions to fractional order differential equations (FODEs) and the approximation of a function’s Caputo fractional derivative. These techniques are based on scattered data interpolation via reproducing kernel Hilbert spaces (RKHSs). Specifically, an RKHS is generated for the purpose of estimating fractional derivatives from the Mittag-Lef...

Zolotarev proved a duality result that relates stable densities with different indices. In this paper, we show how Zolotarev duality leads to some interesting results on fractional diffusion. Fractional diffusion equations employ fractional derivatives in place of the usual integer order derivatives. They govern scaling limits of random walk models, with power law jumps leading to fractional de...

This paper presents a general solution for a space-and time-fractional diffusionwave equation defined in a bounded space domain. The space-and time-fractional derivatives are described in the Caputo sense. The application of Adomian decomposition method, developed for differential equations of integer order, is extended to derive a general solution of the space-and time-fractional diffusionwave...

In this paper, we consider some boundary value problems (BVP) for fractional order partial differential equations ‎(FPDE)‎ with non-local boundary conditions. The solutions of these problems are presented as series solutions analytically via modified Mittag-Leffler functions. These functions have been modified by authors such that their derivatives are invariant with respect to fractional deriv...

Here we derive a multivariate fractional representation formula involving ordinary partial derivatives of …rst order. Then we prove a related multivariate fractional Ostrowski type inequality with respect to uniform norm. 2010 AMS Mathematics Subject Classi…cation : 26A33, 26D10, 26D15.

In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and ...