A Further Extension of the Leibniz Rule to Fractional Derivatives and Its Relation to Parseval’s Formula

1972 ◽  
Vol 3 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Thomas J. Osler
Keyword(s):  
Fractional Derivatives ◽  
Leibniz Rule

A new glance on the Leibniz rule for fractional derivatives

2018 ◽  
Vol 62 ◽  
pp. 244-249 ◽  
Author(s):  
K. Sayevand ◽  
J. Tenreiro Machado ◽  
D. Baleanu
Keyword(s):  
Fractional Derivatives ◽  
Leibniz Rule

scholarly journals Fractional derivatives of certain special functions

2001 ◽  
Vol 32 (2) ◽  
pp. 103-109
Author(s):  
V. B. L. Chaurasia ◽  
Anju Godika
Keyword(s):  
General Class ◽  
Fractional Derivatives ◽  
Special Functions ◽  
Leibniz Rule ◽  
Special Cases ◽  
Derivatives Of

The theorems relating to the fractional derivatives for the multivariable H-function [1,15,17] and a general class of multivariable polynomials [13] have been established in this paper. Use of well known generalized Leibniz rule has been made to derive some theorems. Certain special cases of the main theorems have also been discussed.

scholarly journals An Unified Study of Some Multiple Integrals

2018 ◽  
pp. 37-53
Author(s):  
FY. AY. Ant
Keyword(s):  
Infinite Series ◽  
General Class ◽  
Fractional Derivatives ◽  
Fractional Integration ◽  
Compact Form ◽  
Leibniz Rule ◽  
General Nature ◽  
General Character ◽  
Unified Study ◽  
Multiple Integrals

The object of this paper is to derive three unified fractional derivatives formulae for the Saigo-Maeda operators of fractional integration. The first formula deals with the product of a general class of multivariable polynomials and the multivariable Aleph- function. The second concerns the multivariable polynomials and two multivariable Aleph-functions with the help of the Leibniz rule for fractional derivatives. The last relation also implies the product of a class of multivariable polynomials and the multivariable Aleph-function but it is obtained by the application of the first formula twice and it implicates two independents variables instead of one. The polynomials and the functions have their arguments of the type are quite general nature. These formulae, besides being on very general character have been put in a compact form avoiding the occurrence of infinite series and thus making them put in applications. Our findings provide unifications and extensions of some (known and new) results. We shall give several corollaries and particular cases.

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