Results 21 to 30 of about 56,789 (179)
On fractional Hahn calculus [PDF]
Advances in Difference Equations, 2017 Abstract In this paper, the new concepts of Hahn difference operators are introduced. The properties of fractional Hahn calculus in the sense of a forward Hahn difference operator are introduced and developed.
Thanin Sitthiwirattham +1 more
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Deformation of quantum mechanics in fractional-dimensional space [PDF]
, 2001 A new kind of deformed calculus (the D-deformed calculus) that takes place in fractional-dimensional spaces is presented. The D-deformed calculus is shown to be an appropriate tool for treating fractional-dimensional systems in a simple way and quite ...
A Matos-Abiague +13 more
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General Fractional Vector Calculus [PDF]
Mathematics, 2021 A generalization of fractional vector calculus (FVC) as a self-consistent mathematical theory is proposed to take into account a general form of non-locality in kernels of fractional vector differential and integral operators. Self-consistency involves proving generalizations of all fundamental theorems of vector calculus for generalized kernels of ...
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Review of Some Promising Fractional Physical Models [PDF]
, 2015 Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and ...
Tarasov, Vasily E.
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Fractional-calculus diffusion equation [PDF]
Nonlinear Biomedical Physics, 2010 Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems.The canonical quantization of a system represented classically by one-dimensional Fick's law, and the ...
Hussam Alrabaiah, Abdul-Wali Ajlouni
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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.
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Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions [PDF]
, 2012 We obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter $H>1/2$). This maximum principle specifies a system of equations that the optimal
Han, Yuecai, Hu, Yaozhong, Song, Jian
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The Variable-Order Fractional Calculus of Variations
, 2018 This book intends to deepen the study of the fractional calculus, giving special emphasis to variable-order operators. It is organized in two parts, as follows. In the first part, we review the basic concepts of fractional calculus (Chapter 1) and of the
Almeida, Ricardo +2 more
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A finite element method for time fractional partial differential equations [PDF]
, 2011 This is the authors' PDF version of an article published in Fractional calculus and applied analysis© 2011. The original publication is available at www.springerlink.comThis article considers the finite element method for time fractional differential ...
Ford, Neville J. +2 more
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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
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