Some Fractional q-Integrals and q-Derivatives
نویسندگان
چکیده
منابع مشابه
New Inequalities Using Fractional Q-integrals Theory
The aim of the present paper is to establish some new fractional q-integral inequalities on the specific time scale: Tt0 = {t : t = t0q, n ∈ N} ∪ {0}, where t0 ∈ R, and 0 < q < 1.
متن کاملSOME APPLICATIONS OF FRACTIONAL q-CALCULUS AND FRACTIONAL q-LEIBNIZ RULE
In this article, the fractional q-calculus and fractional q-Leibniz rule are used to generate certain infinite series expansions and transformations relating some of q-special functions of mathematical physics. Some of these expansions and transformations thus generated are known, while others appear to be new.
متن کاملSome Identities on the Generalized q-Bernoulli Numbers and Polynomials Associated with q-Volkenborn Integrals
Let p be a fixed prime number. Throughout this paper, Zp, Qp, C, and Cp will, respectively, denote the ring of p-adic rational integer, the field of p-adic rational numbers, the complex number field, and the completion of algebraic closure of Qp. Let N be the set of natural numbers and Z {0} ∪ N. Let νp be the normalized exponential valuation of Cp with |p|p p−νp p p−1. When one talks of q-exte...
متن کاملOn q–fractional derivatives of Riemann–Liouville and Caputo type
Abstract. Based on the fractional q–integral with the parametric lower limit of integration, we define fractional q–derivative of Riemann–Liouville and Caputo type. The properties are studied separately as well as relations between them. Also, we discuss properties of compositions of these operators. Mathematics Subject Classification: 33D60, 26A33 .
متن کاملThe inequalities for some types of q-integrals
Abstract. We discuss the inequalities for q-integrals because of the fact that the inequalities can be very useful in the future mathematical research. Since q-integral of a function over an interval [a, b] is defined by the difference of two infinite sums, there a lot of unexpected troubles in analyzing analogs of well-known integral inequalities. In this paper, we will signify to some directi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1966
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500011469