Results 51 to 60 of about 621,794 (386)
General fractional calculus and Prabhakar's theory [PDF]
Comm. Nonlinear Sci. Numer. Simulat. 83 (2020) 105114, 2019 General fractional calculus offers an elegant and self-consistent path toward the generalization of fractional calculus to an enhanced class of kernels. Prabhakar's theory can be thought of, to some extent, as an explicit realization of this scheme achieved by merging the Prabhakar (or, three-parameter Mittag-Leffler) function with the general wisdom ...
arxiv +1 more source
A Guide to Special Functions in Fractional Calculus
, 2021 Dedicated to the memory of Professor Richard Askey (1933–2019) and to pay tribute to the Bateman Project. Harry Bateman planned his “shoe-boxes” project (accomplished after his death as Higher Transcendental Functions, Vols.
V. Kiryakova
semanticscholar +1 more source
Fractional derivatives and the fundamental theorem of fractional calculus [PDF]
, 2020 In this paper, we address the one-parameter families of the fractional integrals and derivatives defined on a finite interval. First we remind the reader of the known fact that under some reasonable conditions, there exists precisely one unique family of
Yuri Luchko
semanticscholar +1 more source
N-FRACTIONAL CALCULUS OPERATOR METHOD TO THE EULER EQUATION
Проблемы анализа, 2018 We can obtain the explicit solutions of the Euler equation by using the fractional calculus methods. So, we apply the N operator method in the fractional calculus to solve this equation in this paper.
R. Yilmazer, O. Ozturk
doaj +1 more source
On a New Class of Fractional Calculus of Variations and Related Fractional Differential Equations [PDF]
arXiv, 2021 This paper is concerned with analyzing a class of fractional calculus of variations problems and their associated Euler-Lagrange (fractional differential) equations. Unlike the existing fractional calculus of variations which is based on the classical notion of fractional derivatives, the fractional calculus of variations considered in this paper is ...
arxiv
Concavity in fractional calculus
Filomat, 2018 We discuss a concavity like property for functions u satisfying D?0+u ? C[0, b] with u(0) = 0 and -D?0+u(t) ? 0 for all t ? [0,b]. We develop the property for ? ? (1,2], where D?0+ is the standard Riemann-Liouville fractional derivative. We observe the property is also valid in the case ? = 1. Finally, we show that under certain conditions,
Eloe, Paul W., Neugebauer, Jeffrey T.
openaire +2 more sources
FRACTAL RADIOPHYSICS. Part 3. FRACTIONAL CALCULUS IN ELECTRODYNAMICS [PDF]
Radio Physics and Radio AstronomySubject and Purpose. At the beginning of the 21st century, a fundamentally new scientific direction was formed, currently known as fractal radiophysics.
O. V. Lazorenko, L. F. Chernogor
doaj +1 more source
Journal of Marine Science and Engineering, 2021 An active disturbance rejection control based on fractional calculus is proposed to improve the motion performance and robustness of autonomous underwater vehicle (AUV).
Junhe Wan +6 more
doaj +1 more source
Extended incomplete Riemann-Liouville fractional integral operators and related special functions
Electronic Research Archive, 2022 In this study, we introduce the extended incomplete versions of the Riemann-Liouville (R-L) fractional integral operators and investigate their analytical properties rigorously.
Mehmet Ali Özarslan, Ceren Ustaoğlu
doaj +1 more source
Marvels of fractional calculus
Tbilisi Mathematical Journal, 2017 This is an expository article that describes, in brief, one of the preeminent branch of applicable mathematics, roots of which lie in the nucleus of pure mathematics that ruled the research since past six decades. In writing this article though several important research papers were excised yet attempt is made to retain the beauty of fractional ...
Banerji, P. K., Loonker, Deshna
openaire +3 more sources