Results 11 to 20 of about 415,340 (252)
Fractal Derivative Model for Air Permeability in Hierarchic Porous Media [PDF]
Abstract and Applied Analysis, 2012 Air permeability in hierarchic porous media does not obey Fick's equation or its modification because fractal objects have well-defined geometric properties, which are discrete and discontinuous. We propose a theoretical model dealing with, for the first
Jie Fan, Jihuan He
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Nonlinear Engineering, 2023 A nonlinear Boussinesq equation under fractal fractional Caputo’s derivative is studied. The general series solution is calculated using the double Laplace transform with decomposition. The convergence and stability analyses of the model are investigated
Algahtani Obaid J.
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Chaos in fractional order financial model with fractal–fractional derivatives
Partial Differential Equations in Applied Mathematics, 2023 Recently, a new differential operator which combines fractal differentiation and fractional differentiation with different kernels such as power law, exponential decay, and the Mittag–Leffler function has been introduced.
Krunal B. Kachhia
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A renormalisation approach to excitable reaction-diffusion waves in fractal media [PDF]
, 2003 Of fundamental importance to wave propagation in a wide range of physical phenomena is the structural geometry of the supporting medium. Recently, there have been several investigations on wave propagation in fractal media.
Abdulbake, Janan +2 more
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A powerful and simple frequency formula to nonlinear fractal oscillators
Journal of Low Frequency Noise, Vibration and Active Control, 2021 In this work, a fractal nonlinear oscillator is successfully established by fractal derivative in a fractal space, and its variational principle is obtained by semi-inverse transform method.
Kang-Le Wang, Chun-Fu Wei
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Computation, 2021 In the finance market, the Black–Scholes equation is used to model the price change of the underlying fractal transmission system. Moreover, the fractional differential equations recently are accepted by researchers that fractional differential equations
Sirunya Thanompolkrang +2 more
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Fractal calculus and its geometrical explanation
Results in Physics, 2018 Fractal calculus is very simple but extremely effective to deal with phenomena in hierarchical or porous media. Its operation is almost same with that by the advanced calculus, making it much accessible to all non-mathematicians.
Ji-Huan He
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Reproducing kernel Hilbert space method for solving fractal fractional differential equations
Results in Physics, 2022 Based on reproducing kernel theory, an analytical approach is considered to construct numerical solutions for some basic fractional ordinary differential equations (FODEs, for short) under fractal fractional derivative with the exponential decay kernel ...
Nourhane Attia +4 more
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Alexandria Engineering Journal, 2020 The present paper consider a newly introduced operator known as fractal-fractional where the fractional operator considered is Caputo-Fabrizio. We consider a competition system and propose the field data of banks for 2004–2014 of Indonesia banks of the ...
Abdon Atangana +2 more
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Mathematical Modeling of Breast Cancer Based on the Caputo–Fabrizio Fractal-Fractional Derivative
Fractal and Fractional, 2023 Breast cancer ranks among the most prevalent malignancies affecting the female population and is a prominent contributor to cancer-related mortality. Mathematical modeling is a significant tool that can be employed to comprehend the dynamics of breast ...
Muhammad Idrees +2 more
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