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To the Theory of Differential Inclusions with Caputo Fractional Derivatives
Differential Equations, 2020The paper studies a Cauchy problem associated to fractional differential inclusions of the form \[ ^CD^{\alpha }x(t)\in F(t,x(t)),\quad a.e.\; t\in [t_0,T], \] \[ x(t)=w_0(t),\quad t\in [0,t_0], \] where \(\alpha \in (0,1)\), \(^CD^{\alpha }\) denotes Caputo's fractional derivative, \(F:[0,T]\times {\mathbb{R}}^n\to \mathcal{P}({\mathbb{R}}^n)\) is a ...
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Caputo-Based Fractional Derivative in Fractional Fourier Transform Domain
IEEE Journal on Emerging and Selected Topics in Circuits and Systems, 2013This paper proposes a novel closed-form analytical expression of the fractional derivative of a signal in the Fourier transform (FT) and the fractional Fourier transform (FrFT) domain by utilizing the fundamental principles of the fractional order calculus.
Kulbir Singh +2 more
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Initialization Issues of the Caputo Fractional Derivative
Volume 6: 5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C, 2005The importance of proper initialization in taking into account the history of a system whose time evolution is governed by a differential equation of fractional order, has been established by Lorenzo and Hartley, who also gave the method of properly incorporating the effect of the past (history) by means of an initialization function for the Riemann ...
B. N. Narahari Achar +2 more
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The Peano–Sard theorem for Caputo fractional derivatives and applications
Journal of Computational and Applied MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Arran Fernandez, Suzan Cival Buranay
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Fractional Constrained Systems and Caputo Derivatives
Journal of Computational and Nonlinear Dynamics, 2008During the last few years, remarkable developments have been made in the theory of the fractional variational principles and their applications to control problems and fractional quantization issue. The variational principles have been used in physics to construct the phase space of a fractional dynamical system.
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Convexity in terms of Caputo fractional derivatives
RAIRO - Operations ResearchThe first criterion of convexity states that a differentiable function defined on an open interval is convex if and only if its first derivative is increasing. The second criterion of convexity states that a twice differential function is convex if and only if its second derivative is positive.
Mousaab BOUAFIA +2 more
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Generating Functions and Approximations of the Caputo Fractional Derivative
2023Yuri Dimitrov +4 more
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Dynamical Analysis of Generalized Tumor Model With Caputo Fractional-Order Derivative
Fractal and Fractional, 2023Evren Hincal +2 more
exaly
On the fractional Newton method with Caputo derivatives
Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2022Emine Celik +2 more
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