This work discusses the beginning of fractional calculus and how the Sumudu and Elzaki transforms are applied to fractional derivatives. This approach combines a double Sumudu-Elzaki transform strategy to discover analytic solutions to space-time fractional partial differential equations in Mittag-Leffler functions subject to initial and boundary conditions. Where this method gets closer and closer to the correct answer, and the technique's efficacy is demonstrated using numerical examples performed with Matlab R2015a.

The aim of this paper is to propose an efficient three steps iterative method for finding the zeros of the nonlinear equation f(x)=0 . Starting with a suitably chosen , the method generates a sequence of iterates converging to the root. The convergence analysis is proved to establish its five order of convergence. Several examples are given to illustrate the efficiency of the proposed new method and its comparison with other methods.

In this paper, by using the Banach fixed point theorem, we prove the existence and uniqueness theorem of a fractional Volterra integral equation in the space of Lebesgue integrable 𝐿1(𝑅+) on unbounded interval [0,∞).

Many consumers of electric power have excesses in their electric power consumptions that exceed the permissible limit by the electrical power distribution stations, and then we proposed a validation approach that works intelligently by applying machine learning (ML) technology to teach electrical consumers how to properly consume without wasting energy expended. The validation approach is one of a large combination of intelligent processes related to energy consumption which is called the efficient energy consumption management (EECM) approaches, and it connected with the internet of things (IoT) technology to be linked to Google Firebase Cloud where a utility center used to check whether the consumption of the efficient energy is s

     In this paper, the Adomian decomposition method (ADM) is successfully applied to find the approximate solutions for the system of fuzzy Fredholm integral equations (SFFIEs) and we also study the convergence of the technique. A consistent way to reduce the size of the computation is given to reach the exact solution. One of the best methods adopted to determine the behavior of the approximate solutions. Finally, the problems that have been addressed confirm the validity of the method  applied in this research using a comparison by combining numerical methods such as the Trapezoidal rule and Simpson rule with ADM.

Background: Polyetheretherketone (PEEK) is a promising implant material due to its superior biomechanical strength. However, due to its hydrophobic nature and lack of cellular adhesion properties, it has poor integration with bone tissue. Methods: A fractional CO2 laser was used with various parameters for surface texturing of PEEK substrate to enhance its surface properties. An optical microscope and field-emission scanning electron microscope (FESEM) were used to examine the surface morphology of untextured and laser-textured samples. Energy dispersive X-ray spectroscopy (EDX) was performed to determine the effect of the laser on the microstructure of PEEK. Surface microroughness, atomic force microscopy (AFM), and wettability were invest

This work represents development and implementation a programmable model for evaluating pumping technique and spectroscopic properties of solid state laser, as well as designing and constructing a suitable software program to simulate this techniques . A study of a new approach for Diode Pumped Solid State Laser systems (DPSSL), to build the optimum path technology and to manufacture a new solid state laser gain medium. From this model the threshold input power, output power optimum transmission, slop efficiency and available power were predicted. different systems configuration of diode pumped solid state laser for side pumping, end pump method using different shape type (rod,slab,disk) three main parameters are (energy transfer efficie

    The using of the parametric models and the subsequent estimation methods require the presence of many of the primary conditions to be met by those models to represent the population under study adequately, these prompting researchers to search for more flexible models of parametric models and these models were nonparametric models.

    In this manuscript were compared to the so-called Nadaraya-Watson estimator in two cases (use of fixed bandwidth and variable) through simulation with different models and samples sizes.  Through simulation experiments and the results showed that for the first and second models preferred NW with fixed bandwidth fo