The classical Clark-Ocone theorem states that any random variable F is an element of D-1,2(W) subset of L-2 (F-T, P) can be represented as F = E[F] + integral(T)(0) E[DtF vertical bar F-t]dWd(t), where E[.vertical ...

Analytical solutions of fractional differential equations of two point value problems are considered. An equivalent integral equation of fractional order is used. The nonlinear term is linearized by Adomian polynomials. ...

The fractional chaotic map started to be applied in physics and engineering to properly treat some real-world phenomena. A shuffling method is proposed based on the fractional logistic map. The fractional difference order ...

This paper treats the description of non-differentiable dynamics occurring in complex systems governed by local fractional partial differential equations. The exact solutions of diffusion and relaxation equations with ...

In this paper, we formulate a new nonstandard finite difference (NSFD) scheme to study the dynamic treatments of a class of fractional chaotic systems. To design the new proposed scheme, an appropriate nonlocal framework ...

In this work, the Riccati-Bernoulli sub-ordinary differential equation and modified tanh-coth methods are used to reach soliton solutions of the nonlinear evolution equation. We acquire new types of traveling wave solutions ...

In this paper, we consider a coupled nonlinear Maccaris system (CNMS) which describes the motion of isolated waves localized in a small part of space. There are some integration tools that are adopted to retrieve the ...