This study presents a practical method for solving fractional order delay variational problems. The fractional derivative is given in the Caputo sense. The suggested approach is based on the Laplace transform and the shifted Legendre polynomials by approximating the candidate function by the shifted Legendre series with unknown coefficients yet to be determined. The proposed method converts the fractional order delay variational problem into a set of (n ＋ 1) algebraic equations, where the solution to the resultant equation provides us the unknown coefficients of the terminated series that have been utilized to approximate the solution to the considered variational problem. Illustrative examples are given to show that the recommended appro

In this paper,the homtopy perturbation method (HPM) was applied to obtain the approximate solutions of the fractional order integro-differential equations . The fractional order derivatives and fractional order integral are described in the Caputo and Riemann-Liouville sense respectively. We can easily obtain the solution from convergent the infinite series of HPM . A theorem for convergence and error estimates of the HPM for solving fractional order integro-differential equations was given. Moreover, numerical results show that our theoretical analysis are accurate and the HPM can be considered as a powerful method for solving fractional order integro-diffrential equations.

In this paper we use Bernstein polynomials for deriving the modified Simpson's 3/8 , and the composite modified Simpson's 3/8 to solve one dimensional linear Volterra integral equations of the second kind , and we find that the solution computed by this procedure is very close to exact solution.

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 the knowledge society, artificial intelligence (AI) forms a cornerstone of global education. This quasi-experimental study examines the impact of an Intelligent Adaptive Learning Strategy (IALS) on flexible thinking (FT) and academic achievement among 60 3rd-year undergraduate students at the College of Education/University of Baghdad (experimental n = 30; control n = 30). The IALS was implemented via an AI-supported educational platform, while the control group received conventional instruction. Post-test intervention assessments included an FT test (10 items, content validity = 0.89, Cronbach’s α = 0.87) and an achievement test (10 objective items, α = 0.85). Results revealed statistically significant superiority of the exp

Optimizing system performance in dynamic and heterogeneous environments and the efficient management of computational tasks are crucial. This paper therefore looks at task scheduling and resource allocation algorithms in some depth. The work evaluates five algorithms: Genetic Algorithms (GA), Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), Firefly Algorithm (FA) and Simulated Annealing (SA) across various workloads achieved by varying the task-to-node ratio. The paper identifies Finish Time and Deadline as two key performance metrics for gauging the efficacy of an algorithm, and a comprehensive investigation of the behaviors of these algorithms across different workloads was carried out. Results from the experiment

The gas-lift method is crucial for maintaining oil production, particularly from an established field when the natural energy of the reservoirs is depleted. To maximize oil production, a major field's gas injection rate must be distributed as efficiently as possible across its gas-lift network system. Common gas-lift optimization techniques may lose their effectiveness and become unable to replicate the gas-lift optimum in a large network system due to problems with multi-objective, multi-constrained & restricted gas injection rate distribution. The main objective of the research is to determine the possibility of using the genetic algorithm (GA) technique to achieve the optimum distribution for the continuous gas-lift injectio