This paper is concerned with the backward stochastic differential equations whose generator a weighted fractional Brownian field: Yt=ξ+∫tTYsW(ds,Bs)−∫tTZsdBs, 0≤t≤T, where W (d+1)-parameter field of Hurst parameter H=(H0,H1,⋯,Hd), which provide probabilistic interpretations (Feynman-Kac formulas) for certain linear partial colored space-time noise. Conditions on H and decay rate weight are give...

This paper investigates the solvability, existence and uniqueness of solutions for a class of nonlinear fractional hybrid differential equations with Hilfer fractional derivative in a weighted normed space. The main result is proved by means of a fixed point theorem due to Dhage. An example to illustrate the results is included.

We study Mean Field Games (MFGs) driven by a large class of nonlocal, fractional and anomalous diffusions in the whole space. These non-Gaussian are pure jump Lévy processes with some ?-stable like behaviour. Included Laplace diffusion operators (??)?2, tempered nonsymmetric Finance, spectrally one-sided processes, sums subelliptic different orders. Our main results existence uniqueness classic...

Fractional diffusion equations are abstract partial differential equations that involve fractional derivatives in space and time. They are useful to model anomalous diffusion, where a plume of particles spreads in a different manner than the classical diffusion equation predicts. An initial value problem involving a space-fractional diffusion equation is an abstract Cauchy problem, whose analyt...

Previously, it has been shown that discretising a multi-Hamiltonian PDE in space and time with partitioned Runge–Kutta methods gives rise to a system of equations that formally satisfy a discrete multisymplectic conservation law. However, these studies use the same partitioning of the variables into two partitions in both space and time. This gives rise to a large number of cases to be consider...

Recent years have witnessed a great research boom in soft matter physics. By now, most advances, however, are of empirical results or purely mathematical extensions. The major obstacle is lacking of insights into fundamental physical laws underlying fractal mesostructures of soft matter. This study will use fractional mathematics, which consists of fractal, fractional calculus, fractional Brown...

in this paper, under appropriate oscillating behaviours of the nonlinear term, we prove some multiplicity results for a class of nonlinear fractional equations. these problems have a variational structure and we find three solutions for them by exploiting an abstract result for smooth functionals defined on a reflexive banach space. to make the nonlinear methods work, some careful analysis of t...

In this article we present a new family of high order accurate Arbitrary Lagrangian-Eulerian one-step WENO finite volume schemes for the solution of stiff hyperbolic balance laws. High order accuracy in space is obtained with a standard WENO reconstruction algorithm and high order in time is obtained using the local space-time discontinuous Galerkinmethod recently proposed in [20]. In the Lagra...

In this article, the modified simple equation method has been extended to celebrate the exact solutions of nonlinear partial time-space differential equations of fractional order. Firstly, the fractional complex transformation has been implemented to convert nonlinear partial fractional differential equations into nonlinear ordinary differential equations. Afterwards, modified simple equation m...

In this article, approximate solutions of some PDE fractional order are investi?gated with the help a new semi-analytical method called optimal auxiliary function method. The proposed was tested upon time-fractional Fisher equation, Fornberg-Whitham and Inviscid Burger equation. beauty is that there no need for discretization assumptions small or large parameters provides an ap?proximate soluti...