Results 11 to 20 of about 60,684 (330)
Calculus of Variations with Classical and Fractional Derivatives [PDF]
, 2010 We give a proper fractional extension of the classical calculus of variations. Necessary optimality conditions of Euler-Lagrange type for variational problems containing both classical and fractional derivatives are proved. The fundamental problem of the
Tatiana Odzijewicz, Delfim F. M. Torres
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A Stochastic Fractional Calculus with Applications to Variational Principles
Fractal and Fractional, 2020 We introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes.
Houssine Zine, Delfim F. M. Torres
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A note on the fractional calculus [PDF]
Proceedings of the Edinburgh Mathematical Society, 1978 We prove the following theorem, which settles a conjecture made by J. S. Lew (2, p.379).
John R. McMullen, Donald I. Cartwright
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Complexity and the Fractional Calculus [PDF]
Advances in Mathematical Physics, 2013 We study complex processes whose evolution in time rests on the occurrence of a large and random number of events. The mean time interval between two consecutive critical events is infinite, thereby violating the ergodic condition and activating at the same time a stochastic central limit theorem that supports the hypothesis that the Mittag-Leffler ...
Pramukkul, Pensri +4 more
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Enhancing the Mathematical Theory of Nabla Tempered Fractional Calculus: Several Useful Equations
Fractal and Fractional, 2023 Although many applications of fractional calculus have been reported in literature, modeling the physical world using this technique is still a challenge. One of the main difficulties in solving this problem is that the long memory property is necessary,
Yiheng Wei +3 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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On the solutions of some fractional q-differential equations with the Riemann-Liouville fractional q-derivative [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2021 This paper is devoted to explicit and numerical solutions to linear fractional q -difference equations and the Cauchy type problem associated with the Riemann-Liouville fractional q -derivative in q -calculus.
S. Shaimardan, N.S. Tokmagambetov
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An operational calculus formulation of fractional calculus with general analytic kernels
Electronic Research Archive, 2022 Fractional calculus with analytic kernels provides a general setting of integral and derivative operators that can be connected to Riemann–Liouville fractional calculus via convergent infinite series.
Noosheza Rani , Arran Fernandez
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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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