Abstract This article investigates relative controllability of nonlinear switched fractional systems (SFSs). With the aid Mittag‐Leffler functions and invariant subspace theory, two sufficient necessary conditions for corresponding linear SFSs are first established. Then, piecewise continuous control a novel operator constructed to overcome difficulties arising from switching rules, nonlinearit...

The purpose of this paper is to give formulas and Recurrence relations for the Apostol-Euler numbers polynomials order with complex aid Euler operator partial derivatives generating function. Relations among these neqative integer order, beta-type rational functions, finite combinatorial sums, Stirling numbers, Lah are given. Finally, new classes modification exponential type splines constructed.

In recent years, some Newton-type schemes with noninteger derivatives have been proposed for solving nonlinear transcendental equations by using fractional (Caputo and Riemann–Liouville) conformable derivatives. It has also shown that the methods improve performance of classical schemes. this manuscript, we design point-to-point higher-order multipoint procedures propose a general technique to ...

We consider the task of filtering the noise from images and other types of inputs which are assumed to be piecewise continuous and piecewise monotone. We show that nonlinear diffusion of the data, a powerful filtering method, is too restrictive for such a case, leading to piecewise constant functions. We claim that the piecewise monotonicity can be enhanced by nonlinear diffusion of first parti...

It is well known that, under suitable regularity conditions, the normalized fractional process with parameter d converges weakly to Brownian motion (fBm) for $d>\frac {1}{2}$ . We show any nonnegative integer M , derivatives of order $m=0,1,\dots ,M$ respect jointly converge corresponding fBm. As an illustration, we apply results asymptotic distribution score vectors in multifractional vecto...

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, ...

Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp norms of the function itself as well as its derivatives up to a given order. The derivatives are understood in a suitable weak sense to make the space complete, thus a Banach space. We begin with the classical definition of Sobolev spaces. Definition 1. Let k be a nonnegative integer and let 1 < p < ∞ ...

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...