In this article, we discuss a recently introduced function, Ni(x), and its use in the formulation and solution of non-homogeneous Airy’s differential equation with constant forcing function. Key-words:Airy’s Functions; Scorer Functions; Non-homogeneous Airy’s ODE; Ni(x) Function.

Correspondence: [email protected]. cn Department of Mathematics, Harbin Institute of Technology, Harbin, China Abstract We first introduce and study a new family of weights, the A(a, b, g; E)-class which contains the well-known Ar(E)-weight as a proper subset. Then, as applications of the A(a, b, g ;E)-class, we prove the local and global Poincaré inequalities with the Radon measure for the solut...

Finding optimal data for inpainting is a key problem in the context of partial differential equation-based image compression. We present a new model for optimising the data used for the reconstruction by the underlying homogeneous diffusion process. Our approach is based on an optimal control framework with a strictly convex cost functional containing an L1 term to enforce sparsity of the data ...

The propagation of Love waves in a non-homogeneous layer of finite thickness lying over an isotropic semi-infinite medium is discussed in this study. It is assumed that density and rigidity are space dependent and obey the laws  (1+cosz), μ=μ0 (1+cosz), where ‘’is a scaling parameter. The method of variable separation, substitution method for solving the second order partial differen...

In this paper, the boundary layer flow of an Eyring-Powell non-Newtonian fluid over a linearly stretching sheet is solved using the combination of the quasilinearization method and the Fractional order of Rational Chebyshev function (FRC) collocation method on a semi-infinite domain. The quasilinearization method converts the equation into a sequence of linear equations then, using the FRC coll...

The Richards equation is widely used as a model for the flow of water in unsaturated soils. For modelling one-dimensional flow in a homogeneous soil, this equation can be cast in the form of a specific nonlinear partial differential equation with a time derivative and one spatial derivative. This paper is a survey of recent progress in the pure mathematical analysis of this last equation. The e...

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...

the present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. the proposed scheme is based on laplace transform and new homotopy perturbation methods. the fractional derivatives are considered in caputo sense. to illustrate the ability and reliability of the method some examples are provided. the results ob...

We extend Walsh’s theory of martingale measures in order to deal with hyperbolic stochastic partial differential equations that are second order in time, such as the wave equation and the beam equation, and driven by spatially homogeneous Gaussian noise. For such equations, the fundamental solution can be a distribution in the sense of Schwartz, which appears as an integrand in the reformulatio...