Results 1 to 10 of about 39,805 (286)
Fractal Uncertainty for Transfer Operators [PDF]
International Mathematics Research Notices, 2018 Abstract We show directly that the fractal uncertainty principle of Bourgain–Dyatlov [3] implies that there exists σ > 0 for which the Selberg zeta function (1.2) for a convex co-compact hyperbolic surface has only finitely many zeros with $ \textrm{Re}\, s \geq \frac 12 - \sigma $.
Dyatlov, Semen, Zworski, Maciej
openaire +5 more sources
Studies in fractal–fractional operators with examples
Examples and CounterexamplesBy using the generalization of the gamma function (p-gamma function: Γp(.)), we introduce a generalization of the fractal–fractional calculus which is called p-fractal fractional calculus.
Rabha W. Ibrahim
doaj +2 more sources
Fractalization of Fractional Integral and Composition of Fractal Splines
Chaos Theory and Applications, 2023 The present study perturbs the fractional integral of a continuous function $f$ defined on a real compact interval, say $(\mathcal{I}^vf)$ using a family of fractal functions $(\mathcal{I}^vf)^\alpha$ based on the scaling parameter $\alpha$.
Gowrisankar Arulprakash
doaj +1 more source
The dynamics of dengue infection through fractal-fractional operator with real statistical data
Alexandria Engineering Journal, 2021 The purpose of this work is to analyze the dynamics of dengue fever in newly introduced operator known as fractal-fractional Atangana-Baleanu. Initially, we formulate a new dengue model with hospitalization class of notified infected cases and present ...
Fatmawati, Muhammad Altaf Khan
doaj +1 more source
Results in Physics, 2022 Scientists and researchers are increasingly interested in mathematical modelling of infectious diseases with non-integer order. It is self-evident that a fixed order can only characterize classical models in epidemiology, but models with fractional-order
Joshua Kiddy K. Asamoah
doaj +1 more source
Fractal and fractional dynamics for a 3D autonomous and two-wing smooth chaotic system
Alexandria Engineering Journal, 2020 Some existing chaotic systems cannot display dynamics with attractors showing a fractal representation. This is due, not only to the nature of the phenomenon under description, but also to the type of derivative operator used to express the whole model ...
Emile F. Doungmo Goufo
doaj +1 more source
Analysis of fractal-fractional model of tumor-immune interaction
Results in Physics, 2021 Recently, Atangana proposed new operators by combining the fractional and fractal calculus. These recently proposed operators, referred to as fractal-fractional operators, have been widely used to study the complex dynamics of a problem.
Shabir Ahmad +4 more
doaj +1 more source
Fractal Transformation of Krein–Feller Operators
Zurnal matematiceskoj fiziki, analiza, geometrii, 2023 Summary: We consider a fractal transformed doubly reflected Brownian motion with state space being a Cantor-like set. By applying the theory of fractal transformations as developped by Barnsley, et al., together with an application of a generalised Taylor expression we show that its infinitesimal generator is given in terms of a second order measure ...
Menzel, Max, Freiberg, Uta
openaire +1 more source
Alexandria Engineering Journal, 2022 Fractal fractional operators in Caputo and Caputo-Fabrizio sense are being used in this manuscript to explore the interaction between the immune system and cancer cells.
Shabir Ahmad +3 more
doaj +1 more source
Analysis of Volterra Integrodifferential Equations with the Fractal-Fractional Differential Operator
Complexity, 2023 In this paper, a class of integrodifferential equations with the Caputo fractal-fractional derivative is considered. We study the exact and numerical solutions of the said problem with a fractal-fractional differential operator.
null Kamran +5 more
doaj +1 more source