Abstract
Fractional q-calculus has been investigated and applied in a variety of fields in mathematical areas including fractional q-integral inequalities. In this paper, we study fractional (p,q)-calculus on finite intervals and give some basic properties. In particular, some fractional (p,q)-integral inequalities on finite intervals are proven.
Highlights
Quantum calculus or q-calculus is the study of calculus without limits
As a connection between the fields of mathematics and physics, q-calculus has played a significant role in physics phenomena; for instance, Fock [3] studied the symmetry of hydrogen atoms using the q-difference equation
From Lemma 1, we shall give that which leads to a definition of the fractional ( p, q)integral of the Riemann–Liouville type with the consideration of the n-time as follows: n a I p,q f ( t )
Summary
Quantum calculus or q-calculus is the study of calculus without limits.In the early Eighteenth Century, the well-known mathematician Leonhard Euler (1707–1783) established q-calculus in the way of Newton’s work for infinite series. Quantum calculus or q-calculus is the study of calculus without limits. As a connection between the fields of mathematics and physics, q-calculus has played a significant role in physics phenomena; for instance, Fock [3] studied the symmetry of hydrogen atoms using the q-difference equation. In modern mathematical analysis, q-calculus has many applications such as combinatorics, orthogonal polynomials, basic hypergeometric functions, number theory, quantum theory, mechanics, and the theory of relativity; see [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24] and the references cited therein.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
