A BRIEF STORY ABOUT THE OPERATORS OF THE GENERALIZED FRACTIONAL CALCULUS

By Virginia S. Kiryakova. 2008

133 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/9ee49ea930e5e525a580dba15942c8da6cce9541

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Citations in the corpus

Some generalized fractional calculus operators and their applications in integral equations (2012, background): “A recent survey on generalizations of fractional integrals and derivatives could be found in [7].”
Marichev-Saigo-Maeda fractional integration operators of the Bassel functions (2012, background): “A detailed account of such operators along with their properties and applications can be found in the research monographs by Miller and Ross [14], Kiryakova [9]-[10] and Debnath and Bhatta [1] etc.”
Fractional Calculus: Quo Vadimus? (Where are we Going?) (2015, background): “[43]); – results on classical special functions (special functions of mathematical”
Existence and Uniqueness results for a class of Generalized Fractional Differential Equations (2014, result): “This new derivative has a less complicated form as compared to the corresponding Erdélyi-Kober derivatives, see [15, 16, 20].”
Fractional calculus for power functions and eigenvalues of the fractional Laplacian (2012, result): “For results similar to Theorem 1 concerning fractional derivatives, we refer the reader to [35], [23], [31].”
On the asymptotic stability of linear system of fractional-order difference equations (2013, background): “See, for instance, [2] – [6], [17], [19] and the book by Podlubny [20].”
On History of Mathematical Economics: Application of Fractional Calculus (2019, background): “Operators of generalized fractional calculus [2,10] can be use to describe complex processes with memory and non-locality in real economy.”
Fractional calculus for power functions and eigenvalues of the fractional Laplacian (2012, result): “For results similar to Theorem 1 concerning fractional derivatives, we refer the reader to [35], [23], [31].”
From the hyper-Bessel operators of Dimovski to the generalized fractional calculus (2014, background): “More details on the historical aspects of introduction of the GFC, its concepts and examples can be seen in our previous paper [26].”
Fractional Calculus involving (p, q)-Mathieu Type Series (2020, background): “(for detail see McBride [43], Kalla [44, 45], Kalla and Saxena [46, 47], Saigo [48–50], Saigo and Maeda [51], Kiryakova [32, 52], [53] etc).”