in this paper, a new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (fpdes) in the sense of modified riemann-liouville derivative. with the aid of symbolic computation, we choose the space-time fractional zakharov-kuznetsov-benjamin-bona-mahony (zkbbm) equation in mathematical physics with a source to illustrate the validity a...

We develop and analyze multilevel methods for nonuniformly elliptic operators whose ellipticity holds in a weighted Sobolev space with an A2–Muckenhoupt weight. Using the so-called Xu–Zikatanov (XZ) identity, we derive a nearly uniform convergence result, under the assumption that the underlying mesh is quasi-uniform. We also consider the so-called α-harmonic extension to localize fractional po...

PDE surfaces, whose behavior is governed by Partial Differential Equations (PDEs), have demonstrated many modeling advantages in surface blending, free-form surface modeling, and surface’s aesthetic or functional specifications. Although PDE surfaces can potentially unify geometric attributes and functional constraints for surface design, current PDE-based techniques exhibit certain difficultie...

In this article, we study the numerical approximation of the solution of the Cauchy problem for a multidimensional linear parabolic PDE of second order, with unbounded time and space-dependent coefficients. The PDE free term and the initial data are also allowed to grow. Under the assumption that the PDE does not degenerate, using the L2 theory of solvability in weighted Sobolev spaces, the PDE...

Abstract Aiming at the problems of image edge blur and detail loss in most denoising models, an model based on improved fractional calculus is proposed. Through classification noise, integer order PDE discussed. Based mathematical theory calculus, The by combining texture detection operator, gray value smoothing factor fast algorithm. simulation experiment carried out MATLAB platform. results s...

Abstract The BBM equation is a Hamiltonian PDE which revealed to be very interesting test-model study the transformation property of Gaussian measures along flow, after Tzvetkov (Sigma 3:e28-35). In this paper we with critical dispersion (which Benjamin-Ono type model). We prove that image supported on fractional Sobolev spaces increasing regularity are absolutely continuous, but cannot identif...

In this set of notes we begin the theory of singular integral operators operators which are almost integral operators, except that their kernel K(x, y) just barely fails to be integrable near the diagonal x = y. (This is in contrast to, say, fractional integral operators such as Tf(y) := ∫ Rd 1 |x−y|d−s f(x) dx, whose kernels go to infinity at the diagonal but remain locally integrable.) These ...

background: the increasing use of nuclear radiation for human welfare necessitates the search for new, safe, cost effective radio protectors not only for the personnel’s charged with the responsibility of working or testing with radiations in laboratories, but also for general public. with this view the present study has been undertaken to determine the deleterious effects of sub lethal gamma r...

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...