Abstract This paper is devoted to the discussion of dynamical properties of anisotropic dark energy cosmological model of the universe in a Bianchi type-V space time in the framework of scale covariant theory of gravitation formulated by Canuto et al.(phys.Rev.Lett. 39: 429,1977).A  dark energy cosmological model is presented by solving the field equations of this theory by using some physically viable conditions. The dynamics of the model is  studied  by computing the cosmological parameters, dark energy density, equation of state(EoS) parameter, skewness parameters, deceleration parameter and the jerk parameter. This being a scalar field model gives us the quintessence model of the universe which describes a significant dark energy candidate of our accelerating universe. All the physical quantities discussed are in agreement with the recent cosmological observations.

Abstract This article concerns  with  the  construction of the  analytical traveling  wave so- lutions  for the Generalized-Zakharov System  by the Riccati-Bernoulli Sub- ODE technique. Also, we will discuss this  technique  in random  case by using random  traveling  wave trans- formation  in order  to  find what  is the  effect of the  randomness  input  for this  technique. We presented the Generalized-Zakharov System as an example to show the difference effect between the deterministic and stochastic Riccati-Bernoulli Sub-ODE technique.  The first moment of random solution is computed for different statistical probability distributions.

Abstract In this study, we define the unrestricted Pell and Pell-Lucas quaternions. We give generating functions, Binet formulas and some generalizations of well-known identities such as Vajda’s, Catalan’s, Cassini’s d’Ocagne’s identities.