Results 31 to 40 of about 42,207 (315)
Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics", 2020 In this paper, we introduce a new sort of fractional derivative. For this, we consider the Cauchy's integral formula for derivatives and modify it by using Laplace transform. So, we obtain the fractional derivative formula F(α)(s) = L{(–1)(α)L–1{F(s)}}. Also, we find a relation between Weyl's fractional derivative and the formula above.
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On the oscillation of Hadamard fractional differential equations
Advances in Difference Equations, 2018 Hadamard fractional derivatives are nonlocal fractional derivatives with singular logarithmic kernel with memory, and hence they are suitable to describe complex systems.
Bahaaeldin Abdalla, Thabet Abdeljawad
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Operational Calculus for the General Fractional Derivatives of Arbitrary Order
Mathematics, 2022 In this paper, we deal with the general fractional integrals and the general fractional derivatives of arbitrary order with the kernels from a class of functions that have an integrable singularity of power function type at the origin.
Maryam Al-Kandari +2 more
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E. R. LOVE TYPE LEFT FRACTIONAL INTEGRAL INEQUALITIES
Проблемы анализа, 2020 Here first we derive a general reverse Minkowski integral inequality. Then motivated by the work of E. R. Love [4] on integral inequalities we produce general reverse and direct integral inequalities.
G. A. Anastassiou
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Katugampola Fractional Calculus With Generalized k−Wright Function
European Journal of Mathematical Analysis, 2021 In this article, we present some properties of the Katugampola fractional integrals and derivatives. Also, we study the fractional calculus properties involving Katugampola Fractional integrals and derivatives of generalized k−Wright function nΦkm(z).
Ahmad Y. A. Salamooni, D. D. Pawar
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The Fractional Orthogonal Derivative [PDF]
Mathematics, 2015 This paper builds on the notion of the so-called orthogonal derivative, where an n-th order derivative is approximated by an integral involving an orthogonal polynomial of degree n. This notion was reviewed in great detail in a paper by the author and Koornwinder in 2012.
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Fractional Sums and Differences with Binomial Coefficients
Discrete Dynamics in Nature and Society, 2013 In fractional calculus, there are two approaches to obtain fractional derivatives. The first approach is by iterating the integral and then defining a fractional order by using Cauchy formula to obtain Riemann fractional integrals and derivatives.
Thabet Abdeljawad +3 more
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Mathematics, 2022 In this paper, we first consider the general fractional derivatives of arbitrary order defined in the Riemann–Liouville sense. In particular, we deduce an explicit form of their null space and prove the second fundamental theorem of fractional calculus ...
Yuri Luchko
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Deret Maclaurin Turunan Fraksional Fungsi Inverse Trigonometri dan Radius Kekonverganannya
Jambura Journal of MathematicsFractional derivatives are a generalization of ordinary derivatives to non-integer or fractional orders. This study presents the fractional derivatives of inverse trigonometric functions (arcsin, arccos, and arctan) with the order constraint 0 α ≤ 1 ...
Siti Miftahurrohmah Khoirunisa +2 more
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Comparison principles for fractional differential equations with the Caputo derivatives
Advances in Difference Equations, 2018 In this paper, we deal with comparison principles for fractional differential equations involving the Caputo derivatives of order p with 0≤n ...
Ziqiang Lu, Yuanguo Zhu
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