Variable-order fractional diffusion equation model is a recently developed and promising approach to characterize time-dependent or concentration-dependent anomalous diffusion, process in inhomogeneous porous media. To further study the properties of variable-order time subdiffusion models, efficient numerical schemes are urgently needed. This paper investigates for equations finite domain. Three difference including explicit scheme, implicit scheme Crank–Nicholson studied. Stability...

Based on the best perturbation method, a coupled method is developed to solve inverse source problem of spatial fractional anomalous diffusion equation. The ill-posed first transformed into well-posed by Tikhonov regularization algorithm. Then corresponding direct solved implicit difference in which term estimated method. efficiency and accuracy proposed are demonstrated two numerical examples.

This research paper analyzes the exergy of an absorption refrigeration cycle with a multi mixture working fluid selected as water and lithium-bromide. It relies on fundamental thermodynamic principles, being chiefly first second laws. The destructions have been obtained from different parts cycle; after which several components are analyzed in terms their thermodynamics efficiency. Additionally, efficiency coefficients performance (COP) thoroughly investigated. can be observed results...

Based on the experimental measurement results of fluid particle transverse accelerations in fully developed pipe turbulence published Nature (2001) by La Porta et al, present authors recently develop a multiscale statistical model which considers both normal diffusion molecular scale and anomalous vortex scale. This gives rise to new probability density function, called Power-Stretched Gaussian Distribution (PSGD). In this study, we make further comparison distribution with well-known Lévy...

Models with p-Laplacian operator are common in different scientific fields including; plasma physics, chemical reactions design, biophysics, and many others.In this paper, we investigate existence uniqueness of solution Hyers-Ulam stability for a coupled system fractional differential equations operator.The means that equation has close exact which is generated by the approximate error approximation can be estimated.We use topological degree method provide an expressive example as application work.

In this paper, we develop a new application of the Mittag-Leffler function that will extend to fractional homogeneous differential equations, and propose undetermined coefficient method.A solution is constructed in power series.When very simple ordinary equation satisfied, no matter original linear or nonlinear, method valid, then combine alike terms, compare with identical powers, be obtained.The derivatives are described Caputo sense.To illustrate reliability method, some examples...

New aspects of electron transport in quantum wires with Lévy-type disorder are described. We study the weak scattering and incoherent sequential tunneling one-dimensional systems characterized by a tempered Lévy stable distribution spacing between scatterers or barriers. The generalized Dorokhov–Mello–Pereyra–Kumar equation contains fractional derivative on wire length. solution describes evolution from anomalous conductance to Dorokhov function for long wire. For tunneling, average values...

The approach based on fractional advection–diffusion equations provides an effective and meaningful tool to describe the dispersive transport of charge carriers in disordered semiconductors. A generalization Fick’s law containing Riemann–Liouville derivative is related well-known Fokker–Planck equation, it consistent with universal characteristics observed time-of-flight experiment (ToF). In present paper, we consider generalized Fick laws other forms time operators singular non-singular...

The power law decay is widely observed in lab experiments and field observations. Power-law stability, however, has little been reported the literature. In this study, definition of stability proposed, then via Lyapunov direct method, nonlinear dynamical systems based on Hausdorff derivative investigated. Furthermore, fractal comparison principle introduced to obtain conditions for type. Finally, two examples are given elucidate notion stability.

This paper proposes a new type of fractional differential equation model, named time in which noise term is included the derivative order. The model applied to anomalous relaxation and diffusion processes suffering noisy field. analysis numerical simulation results show that our can well describes feature these processes. We also find scale parameter frequency play crucial role behaviors systems. At end, we recognize some potential applications this model.

Bacterial chemotaxis has recently attracted great interest in purification of groundwater, monitored natural attenuation and contaminant containment. Quantitatively evaluating accurately would lead to a better comprehension the role its broad use applications. Many mathematical, statistical or experimental quantitative parameters have been reported quantify chemotaxis, but how is still uncertain. In this paper, new quantification method based on fractional order signal processing (FOSP)...

Fractional Gaussian noise (fGn) with a constant Hurst parameter H can be used to more accurately characterize the long memory process than traditional short-range dependent stochastic processes, such as Markov, Poisson or ARMA processes. However, ability of fGn is limited for modeling processes prescribed local forms. Therefore, multifractional (mGn) Hölder exponent which varies variable t (usually time), become important both in theory and practical applications. In this paper, by studying...

In this paper, we suggest a robust non-square MIMO (4×8) PID controller for the multi-mode active vibration damping of nanobeam. Nanobeam is modeled by using nonlocal continuum theory Eringen to consider small-scale effects and Euler-Bernoulli beam theory. The problem analyzed free case with Heaviside type disturbance nanobeam without controller. proposed system has four inputs eight outputs, where static decoupling method, decoupled transfer functions obtained. parameters dependig on one...

Summary Drone-based aerial geophysical exploration technology has developed rapidly in recent years, with the advanced progress of manufacturing UAV and detection equipment. In this extended abstract, we present very first Ultra-low-altitude high precision aeromagnetic survey cases using a small unmanned helicopter system. We compare UAV-based results traditional ground-based magnetic two case studies China. The total accuracy measurement is better than ± 1.0nT, find good results....