Results 1 to 10 of about 8,452 (159)
Fractional Integration and Differentiation of the Generalized Mathieu Series [PDF]
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 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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A fractional calculus on arbitrary time scales: Fractional differentiation and fractional integration [PDF]
Signal Processing, 2015 We introduce a general notion of fractional (noninteger) derivative for functions defined on arbitrary time scales. The basic tools for the time-scale fractional calculus (fractional differentiation and fractional integration) are then developed. As particular cases, one obtains the usual time-scale Hilger derivative when the order of differentiation ...
Artur M C Brito da Cruz +1 more
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A high-speed algorithm for computation of fractional differentiation and fractional integration [PDF]
Philosophical Transactions Series A, Mathematical, Physical, and Engineering Sciences, 2013 A high-speed algorithm for computing fractional differentiations and fractional integrations in fractional differential equations is proposed. In this algorithm, the stored data are not the function to be differentiated or integrated but the weighted integrals of the function.
Fukunaga, Masataka, Shimizu, Nobuyuki
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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 integration and differentiation
, 2023 In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of functions and provides a series representation of integration.
Yaremko, Oleg, Yachmenev, Andrey
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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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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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