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.

Fractional generalization of an exterior derivative for calculus of variations is defined. The Hamilton and Lagrange approaches are considered. Fractional Hamilton and Euler–Lagrange equations are derived. Fractional equations are obtained by fractional variation of Lagrangian and Hamiltonian that have only integer derivatives. PACS numbers: 45.20.−d, 45.20.Jj

— This paper is a contribution to the general program of embedding theories of dynamical systems. Following our previous work on the Stochastic embedding theory developed with S. Darses, we define the fractional embedding of differential operators and ordinary differential equations. We construct an operator combining in a symmetric way the left and right (Riemann-Liouville) fractional derivati...

— This paper is a contribution to the general program of embedding theories of dynamical systems. Following our previous work on the Stochastic embedding theory developed with S. Darses, we define the fractional embedding of differential operators and ordinary differential equations. We construct an operator combining in a symmetric way the left and right (Riemann-Liouville) fractional derivati...