Results 11 to 20 of about 372,508 (154)
On applications of Caputo k-fractional derivatives [PDF]
Advances in Difference Equations, 2019 This research explores Caputo k-fractional integral inequalities for functions whose nth order derivatives are absolutely continuous and possess Grüss type variable bounds. Using Chebyshev inequality (Waheed et al. in IEEE Access 7:32137–32145, 2019) for
Ghulam Farid +5 more
doaj +3 more sources
Local density of Caputo-stationary functions in the space of smooth functions [PDF]
ESAIM: COCV, 2017, 2015 We consider the Caputo fractional derivative and say that a function is Caputo-stationary if its Caputo derivative is zero. We then prove that any $C^k\big([0,1]\big)$ function can be approximated in $[0,1]$ by a a function that is Caputo-stationary in $[0,1]$, with initial point $a<0$. Otherwise said, Caputo-stationary functions are dense in $C^k_{loc}
Bucur, Claudia
arxiv +5 more sources
Exact results for a fractional derivative of elementary functions [PDF]
SciPost Physics, 2018 We present exact analytical results for the Caputo fractional derivative of a wide class of elementary functions, including trigonometric and inverse trigonometric, hyperbolic and inverse hyperbolic, Gaussian, quartic Gaussian, and Lorentzian ...
Gavriil Shchedrin, Nathanael C. Smith, Anastasia Gladkina, Lincoln D. Carr
doaj +2 more sources
Solutions of systems with the Caputo-Fabrizio fractional delta derivative on time scales [PDF]
Nonlinear Anal. Hybrid Syst. 32 (2019), 168--176, 2018 Caputo-Fabrizio fractional delta derivatives on an arbitrary time scale are presented. When the time scale is chosen to be the set of real numbers, then the Caputo-Fabrizio fractional derivative is recovered. For isolated or partly continuous and partly discrete, i.e., hybrid time scales, one gets new fractional operators.
Mozyrska, Dorota +2 more
arxiv +3 more sources
Fractional calculus of variations for a combined Caputo derivative [PDF]
Fractional Calculus and Applied Analysis, 2011 We generalize the fractional Caputo derivative to the fractional derivative ${{^CD}^{\alpha,\beta}_{\gamma}}$, which is a convex combination of the left Caputo fractional derivative of order $\alpha$ and the right Caputo fractional derivative of order ...
Malinowska, Agnieszka B. +1 more
core +3 more sources
Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives [PDF]
Commun. Nonlinear Sci. Numer. Simulat. 16 (2011), no. 3,
1490--1500, 2010 We prove optimality conditions for different variational functionals containing left and right Caputo fractional derivatives. A sufficient condition of minimization under an appropriate convexity assumption is given. An Euler-Lagrange equation for functionals where the lower and upper bounds of the integral are distinct of the bounds of the Caputo ...
Agrawal +31 more
arxiv +3 more sources
The sine and cosine diffusive representations for the Caputo fractional derivative [PDF]
arXiv, 2023 As we are aware, various types of methods have been proposed to approximate the Caputo fractional derivative numerically. A common challenge of the methods is the non-local property of the Caputo fractional derivative which leads to the slow and memory consuming methods. Diffusive representation of fractional derivative is an efficient tool to overcome
Dehghan, Mehdi, Khosravian-Arab, Hassan
arxiv +2 more sources
Differential equations with tempered Ψ-Caputo fractional derivative
Mathematical Modelling and Analysis, 2021 In this paper we define a new type of the fractional derivative, which we call tempered Ψ−Caputo fractional derivative. It is a generalization of the tempered Caputo fractional derivative and of the Ψ−Caputo fractional derivative.
Milan Medveď, Eva Brestovanská
doaj +5 more sources
Delay-Dependent Stability Criterion of Caputo Fractional Neural Networks with Distributed Delay [PDF]
Discrete Dynamics in Nature and Society, 2014 This paper is concerned with the finite-time stability of Caputo fractional neural networks with distributed delay. The factors of such systems including Caputo’s fractional derivative and distributed delay are taken into account synchronously.
Abdulaziz Alofi +3 more
doaj +3 more sources
Fractional differential equations with dependence on the Caputo-Katugampola derivative [PDF]
arXiv, 2016 In this paper we present a new type of fractional operator, the Caputo-Katugampola derivative. The Caputo and the Caputo-Hadamard fractional derivatives are special cases of this new operator. An existence and uniqueness theorem for a fractional Cauchy type problem, with dependence on the Caputo--Katugampola derivative, is proven.
Almeida, R. +2 more
arxiv +6 more sources