Results 31 to 40 of about 1,816,969 (371)
Why fractional derivatives with nonsingular kernels should not be used [PDF]
Fractional Calculus and Applied Analysis, 2020 In recent years, many papers discuss the theory and applications of new fractional-order derivatives that are constructed by replacing the singular kernel of the Caputo or Riemann-Liouville derivative by a non-singular (i.e., bounded) kernel.
K. Diethelm +3 more
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International Journal of Analysis and Applications, 2023 This study presents the fractional reduced differential transform method for a nonlinear mutualism model with fractional diffusion. The fractional derivatives are described by Caputo's fractional operator.
Mohamed Ahmed Abdallah +1 more
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Intertwining Certain Fractional Derivatives [PDF]
Potential Analysis, 2011 We obtain an intertwining relation between some Riemann-Liouville operators of order a in (1,2) connecting through a certain multiplicative identity in law the one-dimensional marginals of reflected completely asymmetric a-stable Lévy processes.
Patie, Pierre, Simon, Thomas
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Fractional Coins and Fractional Derivatives [PDF]
Abstract and Applied Analysis, 2013 This paper discusses the fundamentals of negative probabilities and fractional calculus. The historical evolution and the main mathematical concepts are discussed, and several analogies between the two apparently unrelated topics are established. Based on the new conceptual perspective, some experiments are performed shading new light into possible ...
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A note on fractional powers of first-order differential and difference operators in relation to fractional derivatives [PDF]
E-Journal of Analysis and Applied MathematicsThis paper concentrates on fractional derivatives and fractional powers of first-order differential and difference operators. It is illustrated how fractional derivatives are related to fractional powers of a first-order positive operator with boundary ...
Ramil Salimov
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Some types of first order fractional differential equations and their applications [PDF]
E3S Web of Conferences, 2021 This paper uses a new multiplication of fractional functions and chain rule for fractional derivatives, regarding the Jumarie type of modified Riemann-Liouville fractional derivatives to obtain the general solutions of four types of first order ...
Yu Chiihuei
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Research on some types of fractional differential equations which can be transformed into separable variables [PDF]
E3S Web of Conferences, 2021 In this paper, we study some types of fractional differential equations which can be transformed into separable variables, regarding the Jumarie type of modified Riemann-Liouville fractional derivatives.
Yu Chiihuei
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Coupled systems of fractional equations related to sound propagation: analysis and discussion [PDF]
, 2012 In this note we analyse the propagation of a small density perturbation in a one-dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordinary time derivative with the Caputo fractional derivative in the ...
Diethelm K. +6 more
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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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