This work is concerned with the initial boundary value problem for a nonlinear viscoelastic Petrovsky wave equation utt +
, 2u 􀀀,Z t 0 g(t 􀀀,, )
, 2u(,)d,􀀀,
, ut 􀀀,
, utt + utjutjm􀀀, 1 = ujujp􀀀, 1: Under suitable conditions on the relaxation function g, the global ex-istence of solutions is obtained without any relation between m and p. The uniform decay of solutions is proved by adapting the perturbed energy method. For p > m and su, cient conditions on g, an unbound-edness result of solutions is also obtained.

The Haar wavelet collocation with iteration technique is applied for solving a class of time-fractional physical equations. The approximate solutions obtained by two dimensional Haar wavelet with iteration technique are compared with those obtained by analytical methods such as Adomian decomposition method (ADM) and variational iteration method (VIM). The results show that the present scheme is effective and appropriate for obtaining the numerical solution of the timefractional Modified Camassa-Holm equation and Time fractional Modified Degasperis-Procesi equation.

During the past years, a wide range of distinct approaches has been exerted to solve the nonlinear fractional differential equations (NLFDEs). In this paper, the invariant subspace method (ISM) in conjunction with the fractional Sumudu’ s transform (FST) in the conformable context is formally adopted to deal with a nonlinear conformable time-fractional dispersive equation of the Fifth-order. As an outcome, a new exact solution of the model is procured, corroborating the exceptional performance of the hybrid scheme.

The concept of generalized order statistics (GOSs) was introduced as a unified approach to a variety of models of ordered random variables. The purpose of this paper is to investigate conditions on the underlying distribution functions and the parameters on which GOSs are based, to establish Shaked-Shanthikumar multivariate dispersive ordering of GOSs from one sample and Khaledi-Kochar multivariate dispersive ordering of GOSs from two samples. Some applications are also given.