Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution....

the aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (pde) in the electroanalytical chemistry. the space fractional derivative is described in the riemann-liouville sense. in the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the grunwald- letnikov discretization of the ri...

There are many resources useful for processing images, most of them freely available and quite friendly to use. In spite of this abundance of tools, a study of the processing methods is still worthy of efforts. Here, we want to discuss the new possibilities arising from the use of fractional differential calculus. This calculus evolved in the research field of pure mathematics until 1920, when ...

The relation between the heat flux vector and temperature gradient is called heat conduction constitutive model. The most well known constitutive relation in heat transfer is Fourier model which is originally based on experimental observations. This model which is pure diffusive in nature considers the instantaneous flow of heat in the medium in the presence of even a small temperature gradient...

Many different types of fractional calculus have been proposed, which can be organised into some general classes operators. For a unified mathematical theory, results should proved in the most possible setting. Two important fractional-calculus operators are integrals and derivatives with respect to functions (dating back 1970s) those analytic kernels (introduced 2019). To cover both these sett...

An accurate state of charge (SOC) estimation is the basis of the Battery Management System (BMS). In this paper, a new estimation method which considers fractional calculus is proposed to estimate the lithium battery state of charge. Firstly, a modified second-order RC model based on fractional calculus theory is developed to model the lithium battery characteristics. After that, a pulse charac...

We add branching time to the linear discrete event calculus, which yields a formalism for commonsense reasoning that combines the benefits of the situation calculus and the event calculus. We characterize the precise relationship between the linear and branching versions of the discrete event calculus, and prove that a restricted version of the branching discrete event calculus is equivalent to...

Fractional transforms are useful tools for processing of non-stationary signals. The methods of implementing sliding discrete fractional Fourier transform (SDFRFT), sliding discrete fractional cosine transform (SDFRCT) and sliding discrete fractional sine transform (SDFRST) for real time processing of signals are presented. The performances of these sliding transforms, with regard to computatio...