scholarly journals Generalized discrete operators

2021 ◽  
Vol 2 (1) ◽  
pp. 18-23
Author(s):  
Rui Ferreira
Keyword(s):  
Fundamental Theorem ◽  
Fractional Operators ◽  
Fundamental Theorem Of Calculus ◽  
Discrete Operators

We define a class of discrete operators that, in particular, include the delta and nabla fractional operators. Moreover, we prove the fundamental theorem of calculus for these operators.

scholarly journals Integral transforms of the κ-Hilfer fractional derivative

2021 ◽  
Author(s):  
Felix Costa ◽  
Junior Cesar Alves Soares ◽  
Stefânia Jarosz
Keyword(s):  
Fractional Derivative ◽  
Gamma Function ◽  
Fundamental Theorem ◽  
Beta Function ◽  
Integral Transforms ◽  
Fractional Operators ◽  
Riesz Fractional Derivative ◽  
Hilfer Fractional Derivative ◽  
Fundamental Theorem Of Calculus

In this paper, some important properties concerning the κ-Hilfer fractional derivative are discussed. Integral transforms for these operators are derived as particular cases of the Jafari transform. These integral transforms are used to derive a fractional version of the fundamental theorem of calculus. Keywords: Integral transforms, Jafari transform, κ-gamma function, κ-beta function, κ-Hilfer fractional derivative, κ-Riesz fractional derivative, κ-fractional operators.

Teaching the Fundamental Theorem of Calculus: A Historical Reflection

2012 ◽  
Author(s):  
Jorge M. L��pez Fern��ndez ◽  
Omar A. Hern��ndez Rodr��guez
Keyword(s):  
Fundamental Theorem ◽  
Fundamental Theorem Of Calculus ◽  
Historical Reflection
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