Results 1 to 10 of about 2,473 (99)
Generalized Fractional Calculus for Gompertz-Type Models [PDF]
Mathematics, 2021 This paper focuses on the construction of deterministic and stochastic extensions of the Gompertz curve by means of generalized fractional derivatives induced by complete Bernstein functions. Precisely, we first introduce a class of linear stochastic equations involving a generalized fractional integral and we study the properties of its solutions ...
Giacomo Ascione, Enrica Pirozzi
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General Fractional Vector Calculus [PDF]
Mathematics, 2021 A generalization of fractional vector calculus (FVC) as a self-consistent mathematical theory is proposed to take into account a general form of non-locality in kernels of fractional vector differential and integral operators. Self-consistency involves proving generalizations of all fundamental theorems of vector calculus for generalized kernels of ...
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General Fractional Calculus: Multi-Kernel Approach [PDF]
Mathematics, 2021 For the first time, a general fractional calculus of arbitrary order was proposed by Yuri Luchko in 2021. In Luchko works, the proposed approaches to formulate this calculus are based either on the power of one Sonin kernel or the convolution of one Sonin kernel with the kernels of the integer-order integrals.
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Generalized binomials in fractional calculus
Publicationes Mathematicae Debrecen, 2022 We consider a class of generalized binomials emerging in fractional calculus. After establishing some general properties, we focus on a particular yet relevant case, for which we provide several ready-for-use combinatorial identities, including an adapted version of the Pascal's rule.
D'Ovidio, Mirko +2 more
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Generalized Functions for the Fractional Calculus [PDF]
Critical Reviews™ in Biomedical Engineering, 2008 Previous papers have used two important functions for the solution of fractional order differential equations, the Mittag-Leffler functionE(sub q)[at(exp q)](1903a, 1903b, 1905), and the F-function F(sub q)[a,t] of Hartley & Lorenzo (1998). These functions provided direct solution and important understanding for the fundamental linear fractional order ...
Carl F, Lorenzo, Tom T, Hartley
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General fractional calculus and Prabhakar’s theory [PDF]
Communications in Nonlinear Science and Numerical Simulation, 2020 General fractional calculus offers an elegant and self-consistent path toward the generalization of fractional calculus to an enhanced class of kernels. Prabhakar's theory can be thought of, to some extent, as an explicit realization of this scheme achieved by merging the Prabhakar (or, three-parameter Mittag-Leffler) function with the general wisdom ...
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Generalized Multiparameters Fractional Variational Calculus [PDF]
International Journal of Differential Equations, 2012 This paper builds upon our recent paper on generalized fractional variational calculus (FVC). Here, we briefly review some of the fractional derivatives (FDs) that we considered in the past to develop FVC. We first introduce new one parameter generalized fractional derivatives (GFDs) which depend on two functions, and show that many of the one ...
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Weighted Fractional Calculus: A General Class of Operators
Fractal and Fractional, 2022 We conduct a formal study of a particular class of fractional operators, namely weighted fractional calculus, and its extension to the more general class known as weighted fractional calculus with respect to functions. We emphasise the importance of the conjugation relationships with the classical Riemann–Liouville fractional calculus, and use them to ...
Arran Fernandez, Hafiz Muhammad Fahad
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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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Generalized transversality conditions in fractional calculus of variations [PDF]
Communications in Nonlinear Science and Numerical Simulation, 2013 This is a preprint of a paper whose final and definite form will be published in Communications in Nonlinear Science and Numerical Simulation, accepted 14-July ...
Almeida, R, Malinowska, AB
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