Results 11 to 20 of about 2,998 (256)
General Fractional Calculus Operators of Distributed Order
Axioms, 2023 In this paper, two types of general fractional derivatives of distributed order and a corresponding fractional integral of distributed type are defined, and their basic properties are investigated.
Mohammed Al-Refai, Yuri Luchko
doaj +2 more sources
Growth Equation of the General Fractional Calculus [PDF]
Mathematics, 2019 We consider the Cauchy problem ( D ( k ) u ) ( t ) = λ u ( t ) , u ( 0 ) = 1 , where D ( k ) is the general convolutional derivative introduced in the paper (A. N. Kochubei, Integral Equations Oper. Theory 71 (2011),
Anatoly N. Kochubei, Yuri Kondratiev
doaj +3 more sources
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
openaire +2 more sources
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
doaj +1 more source
Mathematics, 2021 General fractional dynamics (GFDynamics) can be viewed as an interdisciplinary science, in which the nonlocal properties of linear and nonlinear dynamical systems are studied by using general fractional calculus, equations with general fractional ...
Vasily E. Tarasov
doaj +1 more source
General Fractional Noether Theorem and Non-Holonomic Action Principle
Mathematics, 2023 Using general fractional calculus (GFC) of the Luchko form and non-holonomic variational equations of Sedov type, generalizations of the standard action principle and first Noether theorem are proposed and proved for non-local (general fractional) non ...
Vasily E. Tarasov
doaj +1 more source
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 ...
Ascione, Giacomo, Pirozzi, Enrica
openaire +4 more sources
Multi-Kernel General Fractional Calculus of Arbitrary Order
Mathematics, 2023 An extension of the general fractional calculus (GFC) of an arbitrary order, proposed by Luchko, is formulated. This extension is also based on a multi-kernel approach, in which the Laplace convolutions of different Sonin kernels are used.
Vasily E. Tarasov
doaj +1 more source
Nonlocal Probability Theory: General Fractional Calculus Approach
Mathematics, 2022 Nonlocal generalization of the standard (classical) probability theory of a continuous distribution on a positive semi-axis is proposed. An approach to the formulation of a nonlocal generalization of the standard probability theory based on the use of ...
Vasily E. Tarasov
doaj +1 more source
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 ...
Ricardo Almeida 0001 +1 more
openaire +4 more sources