In this paper, we will study about Fractional-order partial differential equations in Mathematical Science and introduce analyse fractional calculus with an integral operator that contains the Caputo- Fabrizio’s fractional-order derivative. The advanced method is appropriate union of new transform named as ‘Mohand transform’ homotopy perturbation method. Some numerical examples are used to comm...

The inertia corrected Debye model of rotational Brownian motion of polar molecules is generalized to fractional dynamics (anomalous diffusion) in the context of the fractional Klein-Kramers equation. The fractal generalization of the Gross-Sack solution for the complex dielectric susceptibility chi(omega) for an assembly of fixed axis rotators is given. The high-frequency behavior of chi(omega)...

The anomalous translational diffusion including inertial effects of nonlinear Brownian oscillators in a double well potential V(x)=ax{2}/2+bx{4}/4 is considered. An exact solution of the fractional Klein-Kramers (Fokker-Planck) equation is obtained allowing one to calculate via matrix continued fractions the positional autocorrelation function and dynamic susceptibility describing the position ...

The linear and non-linear Klein-Gordon equations are considered. fractional complex transform is used to convert the on a continuous space/time fractals ones Cantor sets, resultant solved by local reduced differential method. Three examples given show effectiveness of technology.

We propose a covariant definition of the fractional Klein-Gordon equation with long-range interactions independent metric underlying manifold. As an example we consider on AdS$_{2+1}$, computing explicit kernel representation Laplace-Beltrami operator as well two-point propagator equation. Our results suggest that only exists if mass is small compared to inverse AdS radius, presumably because s...

In this paper we prove standard and reversed Strichartz estimates for the Klein--Gordon equation in $\mathbb{R}^{3+1}$. Instead of Fourier theory, our analysis is based on fundamental solutions free equations fractional integrations. final part paper, apply study a semilinear equation.

In this paper we consider a fractional wave equation for hypoelliptic operators with singular mass term depending on the spacial variable and prove that it has very weak solution. Such analysis can be conveniently realised in setting of graded Lie groups. The uniqueness solution, consistency classical solution are also proved, under suitable considerations. This extends improves results obtaine...