Fractional Galilei invariant advection–diffusion (GIADE) equation, along with its more general version that is the GIADE equation nonlinear source term, discretized by coupling weighted and shifted Grünwald difference approximation formulae Crank–Nicolson technique. The new of backward substitution method, a well-established class meshfree methods, proposed for numerical consequent equation. In...

This paper is a comparative study of the multiple RC, Oustaloup and Grünwald–Letnikov approaches for time domain implementations fractional-order battery models. The comparisons are made in terms accuracy, computational burden suitability identification impedance parameters from time-domain measurements. was performed simulation framework focused on set ZARC elements, representing middle freque...

The design of sensor fault detection and isolation (FDI) systems has been studied widely by several authors different fields science (engineering, mathematics, physics) to ensure the continuous operation or processes. This research presents evaluation a system based on discrete fractional-orderhigh-gain observers (DFOHGO) for outlet temperature sensors heat exchanger. formulation fractional-ord...

Underwater images usually suffer from degraded visibility. Light attenuates and scatters in water resulting in low contrast and haziness in the scenes. Therefore, the main problems to be dealt with in underwater environment are poor contrast, non-uniform lighting, haziness and blurring. Hence, in order to study underwater images, it becomes utmost important to extract the invisible or unclear e...

Abstract We study distributed optimal control problems, governed by space-time fractional parabolic equations (STFPEs) involving time-fractional Caputo derivatives and spatial of Sturm-Liouville type. first prove existence uniqueness solutions STFPEs on an open bounded interval their regularity. Then we show to a quadratic problem. derive adjoint problem using the right-Caputo derivative in tim...

In this paper, a weighted and shifted Grünwald-Letnikov difference (WSGD) Legendre spectral method is proposed to solve the two-dimensional nonlinear time fractional mobile/immobile advection-dispersion equation. We introduce correction deal with singularity in time, stability convergence analysis are proven. numerical implementation, fast applied based on globally uniform approximation of trap...

Two implicit finite difference schemes for solving the two-dimensional multi-term time-fractional diffusion equation with variable coefficients are considered in this paper. The orders of Riemann–Liouville fractional time derivatives acting on spatial can be different various directions. By integrating original partial differential first, and second-order approximated by central quotients, then...

Singular source terms in sub-diffusion equations may lead to the unboundedness of solutions, which will bring a severe reduction convergence order existing time-stepping schemes. In this work, we propose two efficient schemes for solving with class mildly singular time. One discretization is based on Grünwald-Letnikov and backward Euler methods. First-order error estimate respect time rigorousl...

Background: solute transport in highly heterogeneous media and even neutron diffusion nuclear environments are among the numerous applications of fractional differential equations (FDEs), being demonstrated by field experiments that concentration profiles exhibit anomalous non-Fickian growth rates so-called “heavy tails”. Methods: a nonlinear-coupled 3D hydro-mechanical model accounting for (FD...