We develop spectral collocation methods for fractional differential equations with variable order with two end-point singularities. Specifically, we derive three-term recurrence relations for both integrals and derivatives of the weighted Jacobi polynomials of the form 1 x μ1 1 Æ x 2P a,b j x a, b, μ1, μ2 Æ1 , which leads to the desired differentiation matrices. We apply the new differentiation...

In this paper, we establish the existence and uniqueness result of the linear Schrodinger equation with Marchaud fractional derivative in Colombeau generalized algebra. The purpose of introducing Marchaud fractional derivative is regularizing it in Colombeau sense.

Discrete-time fractional derivative filters (1-D and 2-D) are shown to be well approximated from a small set of integer derivatives. A fractional derivative of arbitrary order (and, in 2-D, of arbitrary orientation) can therefore be efficiently computed from a linear combination of integer derivatives of the underlying signal or image.

In this paper, we further develop Podlubny's matrix approach to discretization of integrals and derivatives of non-integer order. Numerical integration and differentiation on non-equidistant grids is introduced and illustrated by several examples of numerical solution of differential equations with fractional derivatives of constant orders and with distributed-order derivatives. In this paper, ...

The investigation in the present paper is to obtain certain types of relations for the well known hypergeometric functions by employing the technique of fractional derivative and integral. Mathematics Subject Classification(2010): Primary 42C05, Secondary 33C20, 26A33. Keywords—Fractional Derivatives and Integrals, Hypergeometric functions. THE names fractional calculus is concerned with the ge...

Abstract This article covers the implementation of fractional (non-integer order) differentiation on real data four datasets based stock prices main international indexes: WIG 20, S&P 500, DAX and Nikkei 225. concept has been proposed by Lopez de Prado [5] to find most appropriate balance between zero fully differentiated time series. The aim is making series stationary while keeping its me...