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Yuriy Povstenko, Tamara Kyrylych, Bozena Wozna-Szczesniak and Andrzej Yatsko
The central-symmetric time-fractional heat conduction equation with heat absorption is investigated in a solid with a spherical hole under time-harmonic heat flux at the boundary. The problem is solved using the auxiliary function, for which the Robin-ty...
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Fu-I Chou, Tian-Hsiang Huang, Po-Yuan Yang, Chin-Hsuan Lin, Tzu-Chao Lin, Wen-Hsien Ho and Jyh-Horng Chou
This study proposes a method to improve fractional-order particle swarm optimizer to overcome the shortcomings of traditional swarm algorithms, such as low search accuracy in a high-dimensional space, falling into local minimums, and nonrobust results. I...
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Ronak Pashaei, Mohammad Sadegh Asgari, Amir Pishkoo
Pág. 1 - 7
In this paper the solution of conformable Laplace equation, \frac{\partial^{\alpha}u(x,y)}{\partial x^{\alpha}}+ \frac{\partial^{\alpha}u(x,y)}{\partial y^{\alpha}}=0, where 1 < a = 2 has been deduced by using fractional fourier series and separation ...
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Khalid Hattaf
This paper proposes a new definition of fractional derivative with non-singular kernel in the sense of Caputo which generalizes various forms existing in the literature. Furthermore, the version in the sense of Riemann?Liouville is defined. Moreover, fun...
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Fouad Mohammad Salama,Norhashidah Hj. Mohd Ali
It is time and memory consuming when numerically solving time fractional differential equations as it requires O(N^2) computational cost and O(NM) memory complexity. N and M are the total number of time levels and space grid points, respectively. In this...
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Ajmal Ali,Norhashidah Hj Mohd. Ali
In this paper, we present the preliminary study of the formulation of fractional explicit group (FEG) and fractional explicit de-coupled group (FEDG) iterative methods in solving the two dimensional second order diffusion wave equation of fractional orde...
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Yeshou Xu, Qi He, Ying-Qing Guo, Xing-Huai Huang, Yao-Rong Dong, Zhong-Wei Hu and Jinkoo Kim
Viscoelastic dampers are conventional passive vibration control devices with excellent energy dissipation performance. The fractional derivative has a simple form and high accuracy in the modelling of viscoelastic materials/dampers. The internal variable...
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Bingcheng Huang, Aizhong Lu and Ning Zhang
A solution is proposed for ground surface settlement induced in fractional-generalised Kelvin semi-infinite space by distributed loads, based on the fractional differential theory. The effects of four main parameters?the differential order, the two shear...
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M. Mohamed, S. M. Mabrouk and A. S. Rashed
In recent times, the global community has been faced with the unprecedented challenge of the coronavirus disease (COVID-19) pandemic, which has had a profound and enduring impact on both global health and the global economy. The utilization of mathematic...
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Oscar Herrera-Alcántara
In this paper, fractional calculus principles are considered to implement fractional derivative gradient optimizers for the Tensorflow backend. The performance of these fractional derivative optimizers is compared with that of other well-known ones. Our ...
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Francesca Pitolli, Chiara Sorgentone and Enza Pellegrino
Differential problems with the Riesz derivative in space are widely used to model anomalous diffusion. Although the Riesz?Caputo derivative is more suitable for modeling real phenomena, there are few examples in literature where numerical methods are use...
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Ravi Agarwal, Snezhana Hristova, Donal O?Regan and Kremena Stefanova
The initial value problem for a special type of scalar nonlinear fractional differential equation with a Riemann?Liouville fractional derivative is studied. The main characteristic of the equation is the presence of the supremum of the unknown function o...
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Bakhtiyor Khuzhayorov, Azizbek Usmonov, N.M.A. Nik Long and Bekzodjon Fayziev
In this paper, a problem of anomalous solute transport in a coaxial cylindrical two-zone porous medium with fractal structure is posed and numerically solved. The porous medium is studied in the form of cylinder with two parts: macropore?with high permea...
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Anna Suzuki, Sergei Fomin, Vladimir Chugunov and Toshiyuki Hashida
Deep geological repositories for nuclear wastes consist of both engineered and natural geologic barriers to isolate the radioactive material from the human environment. Inappropriate repositories of nuclear waste would cause severe contamination to nearb...
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Anna Suzuki, Sergei Fomin, Vladimir Chugunov and Toshiyuki Hashida
Deep geological repositories for nuclear wastes consist of both engineered and natural geologic barriers to isolate the radioactive material from the human environment. Inappropriate repositories of nuclear waste would cause severe contamination to nearb...
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Alexandre F. B. Duarte, Jessica de M. Gatti Pereira, Marcelo Kaminski Lenzi, Giane Gonçalves, Roberto Rossato, Ervin Kaminski Lenzi
Pág. 657 - 662
We investigate for the diffusion equation the differences manifested by the solutions when three different types of spatial differential operators of noninteger (or fractional) order are considered for a limited and unlimited region. In all cases, ...
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Angel Golev, Snezhana Hristova and Asen Rahnev
In this paper an algorithm for approximate solving of a boundary value problem for a nonlinear differential equation with a special type of fractional derivative is suggested. This derivative is called a generalized proportional Caputo fractional derivat...
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Sirunya Thanompolkrang, Wannika Sawangtong and Panumart Sawangtong
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Dmitry Gritsenko and Roberto Paoli
Fractional calculus is a relatively old yet emerging field of mathematics with the widest range of engineering and biomedical applications. Despite being an incredibly powerful tool, it, however, requires promotion in the engineering community. Rheology ...
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Dmitry Gritsenko and Roberto Paoli
Pipe flow is one of the most commonly used models to describe fluid dynamics. The concept of fractional derivative has been recently found very useful and much more accurate in predicting dynamics of viscoelastic fluids compared with classic models. In t...
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