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Fractional Integration and Differentiation by new Transformation
Wasit Journal for Pure Sciences, 2023 In opposite to differentiation and integration of integer order, an important type of differentiation and integration is the so - called “ Fractional Calculus (FC) ” in which the differentiation and integration is of non-integer order.
Anfal khalil, Basim Albuohimad
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Multivariable Fractional-Order Controller Design for a Nonlinear Dual-Tank Device
Fractal and Fractional, 2023 Fractional calculus is defined by expanded integer order integration and differentiation. In this paper, multiple mathematical models of a nonlinear dual-tank device are precisely formulated by fractional calculus.
Ryota Kochi, Mingcong Deng
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Spectral analysis of variable-order multi-terms fractional differential equations
Open Physics, 2023 In this work, a numerical scheme based on shifted Jacobi polynomials (SJPs) is deduced for variable-order fractional differential equations (FDEs). We find numerical solution of consider problem of fractional order. The proposed numerical scheme is based
Shah Kamal +3 more
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Fractional-Order Derivatives Defined by Continuous Kernels: Are They Really Too Restrictive?
Fractal and Fractional, 2020 In the field of fractional calculus and applications, a current trend is to propose non-singular kernels for the definition of new fractional integration and differentiation operators.
Jocelyn Sabatier
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Results in Physics, 2023 We consider an epidemiological model that takes into account pathogens in the environment and social distancing. Such model with six classes has been updated with fractional differential operators and piecewise differential operators.
Irem Akbulut Arik +2 more
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The Kuznets Environmental Curve Using Fractional Integration and Long Range Dependence Techniques [PDF]
International Journal of New Political Economy, 2020 This paper investigates empirically the Kuznets environmental curve in nineteen industrialized countries by using updated techniques in time series analysis and based on the concepts of long range dependence and fractional integration. Unlike most of the
Luis A. Gil-Alana
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On the stability of some fractional-order non-autonomous systems
Electronic Journal of Qualitative Theory of Differential Equations, 2007 The fractional calculus (integration and differentiation of fractional-order) is a one of the singular integral and integro-differential operators. In this work a class of fractional-order non-autonomous systems will be considered.
Sheren Ahmed Abd El-Salam +1 more
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Fractional Integration and Differentiation of the Generalized Mathieu Series
Axioms, 2017 We aim to present some formulas for the Saigo hypergeometric fractional integral and differential operators involving the generalized Mathieu series S μ ( r ) , which are expressed in terms of the Hadamard product of the generalized Mathieu ...
Ram K. Saxena, Rakesh K. Parmar
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Fractional State Space Description: A Particular Case of the Volterra Equations
Fractal and Fractional, 2020 To tackle several limitations recently highlighted in the field of fractional differentiation and fractional models, some authors have proposed new kernels for the definition of fractional integration/differentiation operators.
Jocelyn Sabatier
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Why Do Big Data and Machine Learning Entail the Fractional Dynamics?
Entropy, 2021 Fractional-order calculus is about the differentiation and integration of non-integer orders. Fractional calculus (FC) is based on fractional-order thinking (FOT) and has been shown to help us to understand complex systems better, improve the processing ...
Haoyu Niu, YangQuan Chen, Bruce J. West
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