M. Momenzadeh | Searcharxiv

arXiv2020

Study of new class of q-fractional derivative and its properties

There are several approaches to the fractional differential operator. Generalized q-fractional difference operator was defined in the aid of q-iterated Cauchy integral and q-calculus techniques. We introduce Caputo type derivative related to this operator and some properties of this operator as boundness are investigated. Moreover, related q-difference equation is discussed and in the aid of q-successive approximation , existence and uniqueness are studied.

math.GM↗

arXiv2014

On a class of $q$-Bernoulli, $q$-Euler and $q$-Genocchi polynomials

The main purpose of this paper is to introduce and investigate a class of $q$-Bernoulli, $q$-Euler and $q$-Genocchi polynomials. The $q$-analogues of well-known formulas are derived. The $q$-analogue of the Srivastava--Pintér addition theorem is obtained. Some new identities involving $q$-polynomials are proved.

math.CA↗