The Fundamental Theorem of Calculus

2014 ◽  
pp. 249-281
Author(s):  
Peter R. Mercer
Keyword(s):  
Fundamental Theorem ◽  
Fundamental Theorem Of Calculus

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

The Fundamental Theorem of Calculus and Conceptual Explanation

2021 ◽  
pp. 191-204
Author(s):  
Nicholas H. Wasserman ◽  
Timothy Fukawa-Connelly ◽  
Keith Weber ◽  
Juan Pablo Mejia-Ramos ◽  
Stephen Abbott
Keyword(s):  
Fundamental Theorem ◽  
Fundamental Theorem Of Calculus ◽  
Conceptual Explanation
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