An efficient modification and a novel technique combining the homotopy concept with  Adomian decomposition method (ADM) to obtain an accurate analytical solution for Riccati matrix delay differential equation (RMDDE) is introduced  in this paper  . Both methods are very efficient and effective. The whole integral part of ADM is used instead of the integral part of homotopy technique. The major feature in current technique gives us a large convergence region of iterative approximate solutions .The results acquired by this technique give better approximations for a larger region as well as previously. Finally, the results conducted via suggesting an efficient and easy technique, and may be addressed to other non-linear problems.

Abiotic stress-induced genes may lead to understand the response of plants and adaptability to salinity and drought stresses. Differential display reverse transcriptase – polymerase chain reaction (DDRT-PCR) was used to investigate the differences in gene expression between drought- and salinity-stressed plantlets of Ruta graveolens. Direct and stepwise exposures to drought- or salt-responsive genes were screened in R. graveolens plantlets using the DDRT technique. Gene expression was investigated both in the control and in the salt or drought-stressed plantlets and differential banding patterns with different molecular sizes were observed using the primers OPA-01 (646,770 and 983 pb), OPA-08 (593 and 988 pb), OPA-11 (674 and 831 pb

In this paper, the computational method (CM) based on the standard polynomials has been implemented to solve some nonlinear differential equations arising in engineering and applied sciences. Moreover, novel computational methods have been developed in this study by orthogonal base functions, namely Hermite, Legendre, and Bernstein polynomials. The nonlinear problem is successfully converted into a nonlinear algebraic system of equations, which are then solved by Mathematica®12. The developed computational methods (D-CMs) have been applied to solve three applications involving well-known nonlinear problems: the Darcy-Brinkman-Forchheimer equation, the Blasius equation, and the Falkner-Skan equation, and a comparison between the met

In this paper, the dynamic behaviour of the stage-structure prey-predator fractional-order derivative system is considered and discussed. In this model, the Crowley–Martin functional response describes the interaction between mature preys with a predator.  e existence, uniqueness, non-negativity, and the boundedness of solutions are proved. All possible equilibrium points of this system are investigated.  e su‰cient conditions of local stability of equilibrium points for the considered system are determined. Finally, numerical simulation results are carried out to con‹rm the theoretical results.

            The article describes a certain computation method of -arcs to construct the number of distinct -arcs in  for . In this method, a new approach employed to compute the number of -arcs and the number of distinct arcs respectively. This approach is based on choosing the number of inequivalent classes } of -secant distributions that is the number of 4-secant, 3-secant, 2-secant, 1-secant and 0-secant in each process. The maximum size of -arc that has been constructed by this method is . The new method is a new tool to deal with the programming difficulties that sometimes may lead to programming problems represented by the increasing number of arcs. It is essential to reduce the established number of -arcs in each cons

Nowadays, Wheeled Mobile Robots (WMRs) have found many applications as industry, transportation, inspection, and other fields. Therefore, the trajectory tracking control of the nonholonomic wheeled mobile robots have an important problem. This work focus on the application of model-based on Fractional Order  PI^aD^b (FOPID) controller for trajectory tracking problem. The control algorithm based on the errors in postures of mobile robot which feed to FOPID controller to generate correction signals that transport to  torque for each driven wheel, and by means of dynamics model of mobile robot these torques used to compute the linear and angular speed to reach the desired pose. In this work a dynamics model of