In this paper, we investigate two inverse source problems for degenerate time-fractional partial differential equation in rectangular domains. The first problem involves a space-degenerate and the second one time-degenerate equation. Solutions to both are expressed series expansions. For problem, obtained solutions form of Fourier-Legendre series. Convergence uniqueness have been discussed. Fou...

In this present work, we perform a numerical analysis of the value European style options as well sensitivity for option price with respect to some parameters model when underlying process is driven by fractional Lévy process. The given deterministic representation means real valued function satisfying PDE. scheme PDE obtained weighted and shifted Grunwald approximation.

We survey the results in Nane (E. Nane, Higher order PDE’s and iterated processes, Trans. American Math. Soc. (to appear)) and Baeumer, Meerschaert, and Nane (B. Baeumer, M.M. Meerschaert and E. Nane, Brownian subordinators and fractional Cauchy problems: Submitted (2007)) which deal with PDE connection of some iterated processes, and obtain a new probabilistic proof of the equivalence of the h...

We study the perturbation of the two-dimensional stochastic Navier-Stokes equation by a Hilbert-space-valued fractional Brownian noise. Each Hilbert component is a scalar fractional Brownian noise in time, with a common Hurst parameter H and a specific intensity. Because the noise is additive, simple Wiener-type integrals are suffi cient for properly defining the problem. It is resolved by sepa...

Neural networks with radial basis functions method are used to solve a class of initial boundary value of fractional partial differential equations with variable coefficients on a finite domain. It takes the case where a left-handed or right-handed fractional spatial derivative may be present in the partial differential equations. Convergence of this method will be discussed in the paper. A num...

The exact solutions of some conformable time fractional PDEs are presented explicitly. The modified Kudryashov method is applied to construct the solutions to the conformable time fractional Regularized Long WaveBurgers (RLW-Burgers, potential Korteweg-de Vries (KdV) and clannish random walker’s parabolic (CRWP) equations. Initially, the predicted solution in the finite series of a rational for...

although there are many methods for image denoising, but partial differential equation (pde) based denoising attracted much attention in the field of medical image processing such as magnetic resonance imaging (mri). the main advantage of pde-based denoising approach is laid in its ability to smooth image in a nonlinear way, which effectively removes the noise, as well as preserving edge throug...