Results 31 to 40 of about 48,942 (223)
A Caputo fractional derivative-based algorithm for optimization
CoRR, 2021 We propose a novel Caputo fractional derivative-based optimization algorithm. Upon defining the Caputo fractional gradient with respect to the Cartesian coordinate, we present a generic Caputo fractional gradient descent (CFGD) method. We prove that the CFGD yields the steepest descent direction of a locally smoothed objective function.
Yeonjong Shin +2 more
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On Caputo
IEEE Access, 2019 This paper studies the k-fractional analogue of the Caputo fractional derivatives, their properties, and applications. A convolution of two functions instead of the product is analyzed by means of Caputo k-fractional derivatives.
Asif Waheed +5 more
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Caputo-type modification of the Hadamard fractional derivatives [PDF]
Advances in Difference Equations, 2012 Abstract Generalization of fractional differential operators was subjected to an intense debate in the last few years in order to contribute to a deep understanding of the behavior of complex systems with memory effect. In this article, a Caputo-type modification of Hadamard fractional derivatives is introduced. The properties of the modified
Fahd Jarad +2 more
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On a New Modification of the Erdélyi–Kober Fractional Derivative
Fractal and Fractional, 2021 In this paper, we introduce a new Caputo-type modification of the Erdélyi–Kober fractional derivative. We pay attention to how to formulate representations of Erdélyi–Kober fractional integral and derivatives operators.
Zaid Odibat, Dumitru Baleanu
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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. The Cauchy problem for fractional differential equations with this type of derivative is discussed and some existence and ...
Medveď, Milan, Brestovanská, Eva
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Lyapunov Functions to Caputo Fractional Neural Networks with Time-Varying Delays
Axioms, 2018 One of the main properties of solutions of nonlinear Caputo fractional neural networks is stability and often the direct Lyapunov method is used to study stability properties (usually these Lyapunov functions do not depend on the time variable).
Ravi Agarwal +2 more
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Taylor’s Formula for Generalized Weighted Fractional Derivatives with Nonsingular Kernels
Axioms, 2022 We prove a new Taylor’s theorem for generalized weighted fractional calculus with nonsingular kernels. The proof is based on the establishment of new relations for nth-weighted generalized fractional integrals and derivatives. As an application, new mean
Houssine Zine +3 more
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Chaos on the Vallis Model for El Niño with Fractional Operators
Entropy, 2016 The Vallis model for El Niño is an important model describing a very interesting physical problem. The aim of this paper is to investigate and compare the models using both integer and non-integer order derivatives.
Badr Saad T. Alkahtani, Abdon Atangana
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Abstract differential equations and Caputo fractional derivative
Semigroup Forum, 2022 In this work I consider the abstract Cauchy problems with Caputo fractional time derivative of order $α\in(0,1]$, and discuss the continuity of the respective solutions regarding the parameter $α$. I also present a study about the continuity of the Mittag-Leffler families of operators (for $α\in(0,1]$), induced by sectorial operators.
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International Journal of Differential Equations, 2021 In this paper, a class of fractional order differential equation expressed with Atangana–Baleanu Caputo derivative with nonlinear term is discussed.
Meryeme Hassouna +2 more
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