In this paper, we consider a new approach to solve type of partial differential equation by using coupled Laplace transformation with decomposition method to find the exact solution for non–linear non–homogenous equation with initial conditions. The reliability for suggested approach illustrated by solving model equations such as second order linear and nonlinear Klein–Gordon equation. The application results show the efficiency and ability for suggested approach.

Authors in this work design efficient neural networks, which are based on the modified Levenberg - Marquardt (LM) training algorithms to solve non-linear fourth - order three -dimensional partial differential equations in the two kinds in the periodic and in the non-periodic - Periodic. Software reliability growth models are essential tools for monitoring and evaluating the evolution of software reliability. Software defect detection events that occur during testing and operation are often treated as counting processes in many current models. However, when working with large software systems, the error detection process should be viewed as a random process with a continuous state space, since the number of faults found during testin

In this study involves removing of Brilliant Dyes, were which (Brilliant Green {BG} and Brilliant Cresyl Blue {BCB}) by using Iraqi Siliceous Rocks Powder (SRP). Adsorption isotherms were studied and the factors which prefer it, like temperature and salt effect, Adsorption isotherms of dyes, Brilliant Cresyl Blue {BCB} was found to be comparable to Langmuir equation according to Giles classification, isotherms dye Brilliant Green {BG} was found to be comparable to Freundlich equation more than dye Brilliant Blue {BCB} according to Giles classification. The adsorption process on this surface (SRP) studied at different temperatures, the results showed that the adsorption of dyes (BCB, BG) on the surface increased with increased temperature (E

In this article, the solvability of some proposal types of the multi-fractional integro-partial differential system has been discussed in details by using the concept of abstract Cauchy problem and certain semigroup operators and some necessary and sufficient conditions. 

Understanding the effects of fear, quadratic fixed effort harvesting, and predator-dependent refuge are essential topics in ecology. Accordingly, a modified Leslie–Gower prey–predator model incorporating these biological factors is mathematically modeled using the Beddington–DeAngelis type of functional response to describe the predation processes. The model’s qualitative features are investigated, including local equilibria stability, permanence, and global stability. Bifurcation analysis is carried out on the temporal model to identify local bifurcations such as transcritical, saddle-node, and Hopf bifurcation. A comprehensive numerical inquiry is carried out using MATLAB to verify the obtained theoretical findings and und