22 papers · ranked by Valyu relevance
Cypres Verbeeck, Nikolaos Sfakianakis
Integer-order differential operators were originally used to describe local and isotropic effects, in both space and time. However, in fields like biology, the modelling of complex phenomena with spatial heterogeneity necessitates more advanced approaches. The fractional calculus framework provides powerful tools for…
Hamidreza Namazi, Vladimír Kulish
Human brain response is the overall ability of the brain in analyzing internal and external stimuli in the form of transferred energy to the mind/brain phase-space and thus, making the proper decisions. During the last decade scientists discovered about this phenomenon and proposed some models based on computational…
Abdul-Wali MS Ajlouni, Hussam A Al-Rabai'ah
Background Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems. Results The canonical quantization of a system represented…
Rasool Shah, Hassan Khan, Saima Mustafa, Poom Kumam + 1 more
In the present article, fractional-order diffusion equations are solved using the Natural transform decomposition method. The series form solutions are obtained for fractional-order diffusion equations using the proposed method. Some numerical examples are presented to understand the procedure of the Natural transform…
Yuri Luchko
Our starting point is the n-dimensional time-space-fractional partial differential equation (PDE) with the Caputo time-fractional derivative of order $β,0<β<2$ and the fractional spatial derivative (fractional Laplacian) of order $α,0<α\leq2$. For this equation, we first derive some integral representations of the…
Brajesh K. Singh, Vineet K. Srivastava
The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by…
A. Barletta
The analysis of the Rayleigh-B´enard instability due to the mass diffusion in a fluid-saturated horizontal porous layer is reconsidered. The standard diffusion theory based on the variance of the molecular position growing linearly in time is generalised to anomalous diffusion, where the variance is modelled as a…
Asem Wardak, Pulin Gong
Interactions of large numbers of spiking neurons give rise to complex neural dynamics with fluctuations occurring at multiple scales. Understanding the dynamical mechanisms underlying such complex neural dynamics is a long-standing topic of interest in neuroscience, statistical physics and nonlinear dynamics.…
Xiaohua Bi, Huimin Wang, Nikolay Kolev Vitanov, Manuel Torrilhon
The space fractional advection-diffusion equation is a crucial type of fractional partial differential equation, widely used for its ability to more accurately describe natural phenomena. Due to the complexity of analytical approaches, this paper focuses on its numerical investigation. A lattice Boltzmann model for the…
Sadia Arshad, Dumitru Baleanu, Jianfei Huang, Maysaa Mohamed Al Qurashi + 2 more
'Maysaa Mohamed Al Qurashi' 'Yifa Tang' 'Yue Zhao'] In this article, a numerical scheme is formulated and analysed to solve the time-space fractional advection-diffusion equation, where the Riesz derivative and the Caputo derivative are considered in spatial and temporal directions, respectively. The Riesz space…
Daniel Molina-García, Tuan Minh Pham, Paolo Paradisi, Carlo Manzo + 1 more
'Gianni Pagnini'] We present a modelling approach for diffusion in a complex medium characterized by a random length scale. The resulting stochastic process shows subdiffusion with a behavior in qualitative agreement with single particle tracking experiments in living cells, such as ergodicity breaking, pvariation and…
Andrey G. Cherstvy, Wei Wang, Ralf Metzler, Igor M. Sokolov
How related are the ergodic properties of the over- and underdamped Langevin equations driven by fractional Gaussian noise? We here find that for massive particles performing fractional Brownian motion (FBM) inertial effects not only destroy the stylized fact of the equivalence of the ensemble-averaged mean-squared…
Roberto Garra, Elena Issoglio, Giorgio S. Taverna
In this note we consider generalized diffusion equations in which the diffusivity coefficient is not necessarily constant in time, but instead it solves a nonlinear fractional differential equation involving fractional Riemann-Liouville time-derivative. Our main contribution is to highlight the link between these…
William R. Holmes
It has long been known that the complex cellular environment leads to anomalous motion of intracellular particles. At a gross level, this is characterized by mean squared displacements that deviate from the standard linear profile. Statistical analysis of particle trajectories has helped further elucidate how different…
Hosein Nasrolahpour
Understanding biological complexity is one of the most important scientific challenges nowadays. Protein folding is a complex process involving many interactions between the molecules. Fractional calculus is an effective modeling tool for complex systems and processes. In this work we have proposed a new fractional…
A.C. Geiger, C.J. Smith, N. Takanti, D.M. Harmon + 2 more
Fourier transform fluorescence recovery after photobleaching (FT-FRAP) with patterned illumination is theorized and demonstrated for quantitatively evaluating normal and anomalous diffusion. Diffusion characterization is routinely performed to assess mobility in cell biology, pharmacology, and food science.…
Guoxing Lin
Anomalous diffusion has been investigated in many systems. Pulsed field gradient (PFG) anomalous diffusion is much more complicated than PFG normal diffusion. There have been many theoretical and experimental studies for PFG isotropic anomalous diffusion, but there are very few theoretical treatments reported for…
Christopher N. Angstmann, Bruce I. Henry
A standard reaction-diffusion equation consists of two additive terms, a diffusion term and a reaction rate term. The latter term is obtained directly from a reaction rate equation which is itself derived from known reaction kinetics, together with modelling assumptions such as the law of mass action for well-mixed…
Authors not listed
Predicting how often molecules collide in dilute solution remains a long-standing challenge often with several orders of magnitude difference between theoretical values and experimental values also among different experimental values. Traditional frameworks from Smoluchowski and Langmuir rely on the formation of stable…
Jixin Chen
Predicting the reaction kinetics, that is, how fast a reaction can happen in a solution, is essential information for many processes, such as industrial chemical manufacturing, refining, synthesis and separation of petroleum products, environmental processes in air and water, biological reactions in cells, biosensing…
Junkil Park, Aseem Partap Singh Gill, Seyed Mohamad Moosavi, JIHAN KIM
The success of diffusion models in the field of image processing has propelled the creation of software such as Dall-E, Midjourney and Stable Diffusion, which are tools used for text-to-image generations. Mapping this workflow onto materials discovery, a new diffusion model was developed for the generation of pure…
Sarthak Patnaik
We know that the diffusion is defined as the movement of molecules under a potential gradient. It is characterized by the diffusion coefficient. Diffusion coefficient determination can be done via various techniques, but in this paper, we have had a broad look at interferometry based optical methods for diffusion…