One of the two basic theorems in [5] on the existence of solutions of PDEs is improved with the use of a group analysis type argument. Recently, two rather different and general, that is, type independent solution methods have been developed for very large classes of linear and nonlinear systems of PDEs with possibly associated initial and/or boundary conditions. One of them, [5], is using stan...

Comparing with the linear Black–Scholes model, fractional option pricing models are constructed by taking account some more parameters like, for example, transaction cost, so that it becomes difficult to find exact analytical solution. In this paper, we analyze a nonlinear Black and Scholes solution using novel numerical method, based on mixture of efficient techniques. particular, combine (1) ...

The fractional massive Thirring model is a coupled system of nonlinear PDEs emerging in the study complex ultrashort pulse propagation analysis wave functions. This article considers NFMT terms modified Riemann–Liouville derivative. novel travelling solutions considered are investigated by employing an effective analytic approach based on transformation and Jacobi elliptic extended function met...

Parametric PDE techniques, which use partial differential equations (PDEs) defined over a 2D or 3D parametric domain to model graphical objects and processes, can unify geometric attributes and functional constraints of the models. PDEs can also model implicit shapes defined by level sets of scalar intensity fields. In this paper, we present an approach that integrates parametric and implicit t...

Among the properties of systems of analytical partial differential equations (PDEs) which can be studied without explicit integration there are two important ones: the question of their compatibility and the problem of posing of an initial-value problem (Cauchy problem), providing the existence and the uniqueness of an analytical solution. Both of these problems are crucial for the correct form...

This paper presents a self-contained new theory of weak fractional differential calculus in one-dimension. The crux this is the introduction derivative notion which natural generalization integer order derivatives; it also helps to unify multiple existing definitions and characterize what functions are fractionally differentiable. Various rules including fundamental theorem calculus, product ch...

This paper aims to investigate an approximate-analytical and numerical solutions for some 1D 2D dispersive homogeneous non-homogeneous KdV equations by employing two reliable methods namely reduced differential transform method (RDTM) a classical finite-difference method. RDTM provides analytical approximate solution in the form of convergent series. The (FDM) solve is employed primarily checki...

This paper presents a new method to solve the local fractional partial differential equations (LFPDEs) describing fractal vehicular traffic flow. Firstly, existence and uniqueness of solutions LFPDEs were proved then two schemes known as basic (BM) modified variational iteration (LFVIM) developed PDEs. Multiple studies have been reported in literature these problems using iterative methods whic...

Title of dissertation: NONLINEAR EVOLUTIONARY PDEs IN IMAGE PROCESSING AND COMPUTER VISION Kexue Liu, Doctor of Philosophy, 2004 Dissertation directed by: Professor Jian-Guo Liu Department of Mathematics Evolutionary PDE-based methods are widely used in image processing and computer vision. For many of these evolutionary PDEs, there is little or no theory on the existence and regularity of solu...

PDEs belong to a large superfamily [11 different gene families (PDEs 1–11)] of structurally related, functionally distinct, and highly regulated enzymes (Francis et al., 2001). Most PDE families comprise more than one gene ( 20 PDE genes), which generate multiple protein products ( 50 PDE proteins) via alternative mRNA splicing or use of different promoters/transcription initiation sites. Most ...