In the present work, discrete homotopy analysis method is applied to solve nabla time-fractionalpartial difference equations. Fractional operator considered in Caputo’s sense. We apply thediscrete fractional initial value problems. Obtained solutions involvean auxiliary parameter h, which we can determine. Thus, it may be concluded that homotopyanalysis a very powerful and successful analytical...

This work aims to present a study on the stability analysis of linear and nonlinear incommensurate h-nabla fractional-order difference systems. Several theoretical results are inferred with help using some schemes, such as Z-transform method, Cauchy–Hadamard theorem, Taylor development approach, final-value theorem Banach fixed point theorem. These verified numerically via two illustrative nume...

in this paper, we investigate the existence of solution for a k-dimensional system of three points nabla fractional finite difference equations. also, we present an example to illustrate our result.

We introduce non-commutative analogs of k-Schur functions and prove that their images by the noncommutative nabla operator H is ribbon Schur positive, up to a global sign. Inspired by these results, we define new filtrations of the usual (q, t)-Catalan polynomials by computing the image of certain commutative k-Schur functions by the commutative nabla operator∇. In some particular cases, we giv...

In this paper, we investigate the existence of solution for a k-dimensional system of three points nabla fractional finite difference equations. Also, we present an example to illustrate our result.

We conjecture a combinatorial formula for the monomial expansion of the image of any Schur function under the Bergeron-Garsia nabla operator. The formula involves nested labelled Dyck paths weighted by area and a suitable “diagonal inversion” statistic. Our model includes as special cases many previous conjectures connecting the nabla operator to quantum lattice paths. The combinatorics of the ...

The objective of this paper is twofold: (i) to survey existing results of generalized polynomials on time scales, covering definitions and properties for both delta and nabla derivatives; (ii) to extend previous results by using the more general notion of diamond-alpha derivative on time scales. We introduce a new notion of combined-polynomial series on a time scale, as a convex linear combinat...

In this article, we present a two-point boundary value problem with separated conditions for finite nabla fractional difference equation. First, construct an associated Green’s function as series of functions the help spectral theory, and obtain some its properties. Under suitable on nonlinear part equation, deduce two existence results considered by means Leray–Schauder fixed point theorems. W...