The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.

Milling process is a common machining operation that is used in the manufacturing of complex surfaces. Machining-induced residual stresses (RS) have a great impact on the performance of machined components and the surface quality in face milling operations with parameter cutting. The properties of engineering material as well as structural components, specifically fatigue life, deformation, impact resistance, corrosion resistance, and brittle fracture, can all be significantly influenced by residual stresses. Accordingly, controlling the distribution of residual stresses is indeed important to protect the piece and avoid failure. Most of the previous works inspected the material properties, tool parameters, or cutting parameters, bu

Many objective optimizations (MaOO) algorithms that intends to solve problems with many objectives (MaOP) (i.e., the problem with more than three objectives) are widely used in various areas such as industrial manufacturing, transportation, sustainability, and even in the medical sector.  Various approaches of MaOO algorithms are available and employed to handle different MaOP cases. In contrast, the performance of the MaOO algorithms assesses based on the balance between the convergence and diversity of the non-dominated solutions measured using different evaluation criteria of the quality performance indicators. Although many evaluation criteria are available, yet most of the evaluation and benchmarking of the MaOO with state-of-art a

Five levels of Zn-EDTA fertilizer and foliar application of boron were used to study the local rice response through studying of some vegetative and reproductive growth characters, by conducting two field experiments at Kanipanka Agricultural Research Station during the summer season of 2004 by using RCBD with three replications. Significant differences were found in studied characters, there were increase in the number of days from seeding to 50% flowering (94.330-96.233) days, from 50% flowering to physiological maturity (37.50-38.28) days, plant height (82.50-91.423) cm and LAI (5.441-7.525). Reproductive characters such as number of grains panicle-1 (74.11-85.88), number of panicles m-2 (321.00-426.083), biological yield (8166.166-11082

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.

   The economical and highly performed anode material is the critical factor affecting the efficiency of electro-oxidation toward organics. The present study aimed to detect the best conditions to prepare Mn-Co oxide composite anode for the electro-oxidation of phenol. Deposition of Mn-Co oxide onto graphite substrate was investigated at 25, 30, and 35 mA/cm² to detect the best conditions for deposition.  The structure and the crystal size of the Mn-Co oxide composite electrode were examined by using an X-Ray diffractometer (XRD), the morphological properties of the prepared electrode were studied by scanning electron microscopy (SEM) and Atomic force microscopy (AFM) techniques, and the chemical composition of the various