BACKGROUND AND PURPOSE Imaging-based tumor grading is highly desirable but faces challenges in sensitivity, specificity, and diagnostic accuracy. A recently proposed diffusion imaging method by using a fractional order calculus model offers a set of new parameters to probe not only the diffusion process itself but also intravoxel tissue structures, providing new opportunities for noninvasive tu...

In this note, we review some important results on wavelets, together with their main applications. Similarly, present the fractional calculus and current applications in pure applied science. We conclude paper showing close interconnection between wavelet analysis calculus.

The paper discusses fractional integrals and derivatives appearing in the so-called (q, h)-calculus which is reduced for h = 0 to quantum calculus q 1 difference calculus. We introduce delta as well nabla version of these notions present their basic properties. Furthermore, we give comparisons with known results discuss possible extensions more general settings.

Out of equilibrium states in glasses and crystals have been a major topic research condensed-matter physics for many years, the idea time has triggered flurry new research. Here, we provide first description recently conjectured Time Glasses using fractional calculus methods. An exactly solvable effective theory is introduced, with continuous parameter describing transition from liquid through ...

Tempered fractional Brownian motion is obtained when the power law kernel in the moving average representation of a fractional Brownian motion is multiplied by an exponential tempering factor. This paper develops the theory of stochastic integrals for tempered fractional Brownian motion. Along the way, we develop some basic results on tempered fractional calculus.