Fractional Sums and Differences with Binomial Coefficients
Joint Authors
Jarad, Fahd
Abdeljawad (Maraaba), T.
Baleanu, Dumitru
Agarwal, Ravi P.
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-05-20
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
In fractional calculus, there are two approaches to obtain fractional derivatives.
The first approach is by iterating the integral and then defining a fractional order by using Cauchy formula to obtain Riemann fractional integrals and derivatives.
The second approach is by iterating the derivative and then defining a fractional order by making use of the binomial theorem to obtain Grünwald-Letnikov fractional derivatives.
In this paper we formulate the delta and nabla discrete versions for left and right fractional integrals and derivatives representing the second approach.
Then, we use the discrete version of the Q-operator and some discrete fractional dual identities to prove that the presented fractional differences and sums coincide with the discrete Riemann ones describing the first approach.
American Psychological Association (APA)
Abdeljawad (Maraaba), T.& Baleanu, Dumitru& Jarad, Fahd& Agarwal, Ravi P.. 2013. Fractional Sums and Differences with Binomial Coefficients. Discrete Dynamics in Nature and Society،Vol. 2013, no. 2013, pp.1-6.
https://search.emarefa.net/detail/BIM-446656
Modern Language Association (MLA)
Abdeljawad (Maraaba), T.…[et al.]. Fractional Sums and Differences with Binomial Coefficients. Discrete Dynamics in Nature and Society No. 2013 (2013), pp.1-6.
https://search.emarefa.net/detail/BIM-446656
American Medical Association (AMA)
Abdeljawad (Maraaba), T.& Baleanu, Dumitru& Jarad, Fahd& Agarwal, Ravi P.. Fractional Sums and Differences with Binomial Coefficients. Discrete Dynamics in Nature and Society. 2013. Vol. 2013, no. 2013, pp.1-6.
https://search.emarefa.net/detail/BIM-446656
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-446656