Results 31 to 40 of about 857,826 (292)
, 2023 : In this paper, based on Jumarie’s modified Riemann-Liouville (R-L) fractional calculus, we find the solution of some type of improper fractional integral.
Chii-Huei Yu
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Discrete Laplacian Operator and Its Applications in Signal Processing
IEEE Access, 2020 Fractional calculus has increased in popularity in recent years, as the number of its applications in different fields has increased. Compared to the traditional operations in calculus (integration and differentiation) which are uniquely defined, the ...
Waseem Waheed, Guang Deng, Bo Liu
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Implementation of fractional order integrator/differentiator on field programmable gate array
Alexandria Engineering Journal, 2016 Concept of fractional order calculus is as old as the regular calculus. With the advent of high speed and cost effective computing power, now it is possible to model the real world control and signal processing problems using fractional order calculus ...
K.P.S. Rana +3 more
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Fractional Calculus - Theory and Applications
, 2022 In recent years, fractional calculus has led to tremendous progress in various areas of science and mathematics. New definitions of fractional derivatives and integrals have been uncovered, extending their classical definitions in various ways. Moreover,
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Fractional Integrals and Derivatives: “True” versus “False”
Mathematics, 2023 Within the last few years, many of the efforts of the fractional calculus (FC) community have been directed towards clarifying the nature and essential properties of the operators known as fractional integrals and derivatives [...]
Yuri Luchko
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Fractal and FractionalTraditional operational calculus, while intuitive and effective in addressing problems in physical fractal spaces, often lacks the rigorous mathematical foundation needed for fractional operations, sometimes resulting in inconsistent outcomes. To address
Zelin Liu, Xiaobin Yu, Yajun Yin
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A modification to the conformable fractional calculus with some applications
Alexandria Engineering Journal, 2020 In the conformable fractional calculus, TαTβ≠TβTα and IαIβ≠IβIα, where Tα and Iα are conformable fractional differential and integral operators, respectively. Also, Tβ≠Tnα and Iβ≠Inα, where β=nα for some n∈N.
Ahmad El-Ajou
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Kronecker operational matrices for fractional calculus and some applications [PDF]
Applied Mathematics and Computation, 2007 The authors study several operational matrices for integration and differentiation. For some applications, it is often not necessary to compute exact solutions, approximate solutions are sufficient. The given method is extended to find the exact and numerical solutions of the general system matrix convolution differential equations. Several systems are
Adem Kiliçman +1 more
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ДРОБНОЕ ИСЧИСЛЕНИЕ И АППРОКСИМАЦИОННЫЕ МЕТОДЫ В МОДЕЛИРОВАНИИ ДИНАМИЧЕСКИХ СИСТЕМ [PDF]
, 2008 Книга посвящена аппроксимационно-операционным методам моделирования динамических систем дробного и смешанного порядков. Рассмотрены методы аппроксимации сигналов обобщенными полиномами с различными системами базисных функций, построение на основе этих ...
Симак, Лилия Алексеевна +1 more
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Research on Application of Fractional Calculus Operator in Image Underlying Processing
Fractal and FractionalFractional calculus extends traditional, integer-based calculus to include non-integer orders, offering a powerful tool for a range of engineering applications, including image processing.
Guo Huang +5 more
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