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

Mathematics

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