Results 31 to 40 of about 6,876 (298)
Simulation of fractionally damped mechanical systems by means of a Newmark-diffusive scheme [PDF]
, 2010 A Newmark-diffusive scheme is presented for the time-domain solution of dynamic systems containing fractional derivatives. This scheme combines a classical Newmark time-integration method used to solve second-order mechanical systems (obtained for ...
Matignon, Denis +3 more
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Fractional derivative generalization of Noether’s theorem
Open Mathematics, 2015 Abstract The symmetry of the Bagley–Torvik equation is investigated by using the Lie group analysis method. The Bagley–Torvik equation in the sense of the Riemann–Liouville derivatives is considered. Then we prove a Noetherlike theorem for fractional Lagrangian densities with the Riemann-Liouville fractional derivative and few examples ...
Khorshidi Maryam +2 more
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On the Basic Theory of Some Generalized and Fractional Derivatives
Fractal and Fractional, 2022 We continue the development of the basic theory of generalized derivatives as introduced and give some of their applications. In particular, we formulate necessary conditions for extrema, Rolle’s theorem, the mean value theorem, the fundamental theorem of calculus, integration by parts, along with an existence and uniqueness theorem for a generalized ...
Leila Gholizadeh Zivlaei +1 more
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Existence in the Large for Caputo Fractional Multi-Order Systems with Initial Conditions
Foundations, 2023 One of the key applications of the Caputo fractional derivative is that the fractional order of the derivative can be utilized as a parameter to improve the mathematical model by comparing it to real data.
Zachary Denton, Aghalaya S. Vatsala
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Generalized Laplace transform and tempered Ψ-Caputo fractional derivative
, 2023 In this paper, images of the tempered Ψ-Hilfer fractional integral and the tempered Ψ-Caputo fractional derivative under the generalized Laplace transform are derived.
Pospíšil, Michal, Medveď, Milan
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The General Fractional Derivative and Related Fractional Differential Equations [PDF]
Mathematics, 2020 In this survey paper, we start with a discussion of the general fractional derivative (GFD) introduced by A. Kochubei in his recent publications. In particular, a connection of this derivative to the corresponding fractional integral and the Sonine relation for their kernels are presented.
Yuri Luchko, Masahiro Yamamoto
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Caputo Type Fractional Differentiation for the Extended Generalized Mittag-Leffler Function
, 2023 The goal of this paper is to develop some differential equation formulas for the extended generalized Mittag-Leffler function (EGMLF) using Caputo type Marichev-Saigo-Maeda (MSM) fractional derivative operators involving the third Appell function as ...
UÇAR, FARUK
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Study of generalized type K-fractional derivatives [PDF]
Advances in Difference Equations, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Azam, M. K., Farid, G., Rehman, M. A.
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Advances in Difference Equations, 2018 The generalized Caputo fractional derivative is a name attributed to the Caputo version of the generalized fractional derivative introduced in Jarad et al. (J. Nonlinear Sci. Appl. 10:2607–2619, 2017).
Y. Y. Gambo +3 more
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Open Physics, 2022 In this article, we extend the generalized invexity and duality results for multiobjective variational problems with fractional derivative pertaining to an exponential kernel by using the concept of weak minima.
Dubey Ved Prakash +4 more
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