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Second-order asymptotics of fractional Gagliardo seminorms as s → 1 - and convergence of the associated gradient flows. [PDF]
Fract Calc Appl AnalKubin A, Pagliari V, Tribuzio A.
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Fractional Calculus : Generalized Integral and Derivative (On Fractional Calculus and Its Applications)openaire +1 more source
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 ...
Andrea Giusti
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On fractional calculus with general analytic kernels [PDF]
Applied Mathematics and Computation, 2019 Many possible definitions have been proposed for fractional derivatives and integrals, starting from the classical Riemann-Liouville formula and its generalisations and modifying it by replacing the power function kernel with other kernel functions.
Dumitru Baleanu +2 more
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Fractional calculus and generalized Rodrigues formula
Applied Mathematics and Computation, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Saad Zagloul Rida, Ahmed M. A. El-Sayed
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Generalized Memory: Fractional Calculus Approach [PDF]
Fractal and Fractional, 2018 The memory means an existence of output (response, endogenous variable) at the present time that depends on the history of the change of the input (impact, exogenous variable) on a finite (or infinite) time interval. The memory can be described by the function that is called the memory function, which is a kernel of the integro-differential operator ...
Vasily E Tarasov
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Generalized Fractional Calculus and Behaviors
2020We show in this chapter that the module-behavior duality can also be applied to fractional or symbolic calculus, to suitably defined fractional behaviors and to the constructive solution of general fractional differential systems. We generalize the standard fractional calculus considerably.
Ulrich Oberst +2 more
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INITIALIZATION, CONCEPTUALIZATION, AND APPLICATION IN THE GENERALIZED (FRACTIONAL) CALCULUS
Critical Reviews™ in Biomedical Engineering, 2007This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to engineering and the sciences. A modified set of definitions for the fractional calculus is provided which formally include the effects of initialization.
Carl F, Lorenzo, Tom T, Hartley
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On univariate fractional calculus with general bivariate analytic kernels
Computational and Applied Mathematics, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sunday Simon Isah +2 more
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FOUNDATION OF THE FRACTIONAL CALCULUS IN GENERALIZED FUNCTION ALGEBRAS
Analysis and Applications, 2012We introduce an approach to fractional derivatives involving singularities based on the theory of algebras of generalized functions in the sense of Colombeau. We are interested in solving fractional nonlinear ODEs and PDEs with singularities with a lack of solutions in the space of classical functions or distributions.
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