Results 141 to 150 of about 372,508 (154)

On a novel fractional Caputo-derivative Orlicz space

In this work, we aim to explore whether a novel type of fractional space can be defined using Orlicz spaces and fractional calculus. This inquiry is fruitful, as extending classical results to new contexts can lead to a better and deeper understanding of those classical results.
Ayoub, Kasmi, Houssine, Azroul El, Mohammed, Shimi   +2 more
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Extended Caputo k-type fractional derivative operator and its properties

Partial Differential Equations in Applied Mathematics
In this paper, we present some extensions of the k-hypergeometric functions and then develop the extended Caputo k-type fractional derivative operator by using two parameters k-Mittag–Leffler function.
Parik Laxmi, Shilpi Jain, Praveen Agarwal   +2 more
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On a Caputo-type fractional derivative

Advances in Pure and Applied Mathematics, 2019
Abstract In this paper, we present a new differential operator of arbitrary order defined by means of a Caputo-type modification of the generalized fractional derivative recently proposed by Katugampola. The generalized fractional derivative, when convenient limits are considered, recovers the Riemann–Liouville and the Hadamard derivatives ...
Daniela Oliveira, Edmundo Capelas de Oliveira   +1 more
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Fractional viscoelastic models with Caputo generalized fractional derivative

Mathematical Methods in the Applied Sciences, 2021
This article focuses on fractional Maxwell model of viscoelastic materials, which are a generalization of classic Maxwell model to noninteger order derivatives. We present and discuss formulations of the fractional order viscoelastic model and give physical interpretations of the model by using viscoelastic functions.
Nikita Bhangale, Krunal B. Kachhia, J. F. Gómez‐Aguilar   +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, 2005
The 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 ...
Carl F. Lorenzo, Tom T. Hartley, B. N. Narahari Achar   +2 more
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Automatic initialization of the Caputo fractional derivative

IEEE Conference on Decision and Control and European Control Conference, 2011
Initialization of Riemann-Liouville and Caputo fractional derivatives remains an open research topic. These fractional derivatives are fundamentally related to fractional integration operators, so their initial conditions are the initial state vector of the associated fractional integrators.
Nezha Maamri, Alain Oustaloup, J-C. Trigeassou   +2 more
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A new fractional integral associated with the Caputo–Fabrizio fractional derivative

Rendiconti del Circolo Matematico di Palermo Series 2, 2020
In this article, we introduce a new fractional integral (FI) associated with the Caputo–Fabrizio fractional derivative. As a theoretical example, we have solved a fractional boundary value problem (BVP) using the proposed FI. A Matlab script to solve this BVP is also provided.
M. Moumen Bekkouche, H. Guebbai, M. Kurulay, S. Benmahmoud   +3 more
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Approximations of fractional integrals and Caputo fractional derivatives

Applied Mathematics and Computation, 2006
Abstract In this paper we propose two algorithms for numerical fractional integration and Caputo fractional differentiation. We present a modification of trapezoidal rule that is used to approximate finite integrals, the new modification extends the application of the rule to approximate integrals of arbitrary order α > 0.
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On a New Extension of Caputo Fractional Derivative Operator

2017
In this paper, by using a generalization of beta function we introduced a new extension of Caputo fractional derivative operator and obtained some of its properties. With the help of this extended fractional derivative operator, we also defined new extensions of some hypergeometric functions and determined their integral representations, linear and ...
Kıymaz İ.O., Agarwal P., Jain S., Çetinkaya A.   +3 more
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Fractional Constrained Systems and Caputo Derivatives

Journal of Computational and Nonlinear Dynamics, 2008
During 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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