The fractional order partial differential equations (FPDEs) are generalizations of classical partial differential equations (PDEs). In this paper we examine the stability of the explicit and implicit finite difference methods to solve the initial-boundary value problem of the hyperbolic for one-sided and two sided fractional order partial differential equations (FPDEs). The stability (and convergence) result of this problem is discussed by using the Fourier series method (Von Neumanns Method).

  This study was designed to show the roles of vitamin D as immune-modulatory agent in serum type II Diabetes Mellitus Patients collected from type II Diabetes Mellitus and controls. They have been classified into two groups as the following: 1) Patients of type II DM group includes (20) individuals from both sexes with age range (35–65) years. 2) Control group: includes (20) healthy individuals from both sexes, with age range (30 – 45) years and no previous disease which may interfere with the parameters analyzed in this research. All the blood samples were analyzed for vitamin D3, albumin, C- reactive protein (CRP), erythrocyte sedimentation rate (ESR), immunoglobulins (IgG, IgM, IgA),  α1- antitrypsin and to

Continuous escalation of the cost of generating energy is preceded by the fact of scary depletion of the energy reserve of the fossil fuels and pollution of the environment as developed and developing countries burn these fuels. To meet the challenge of the impending energy crisis, renewable energy has been growing rapidly in the last decade. Among the renewable energy sources, solar energy is the most extensively available energy, has the least effect on the environment, and is very efficient in terms of energy conversion. Thus, solar energy has become one of the preferred sources of renewable energy. Flat-plate solar collectors are one of the extensively-used and well-known types of solar collectors. However, the effectiveness of the coll

This research paper studies the use of an environmentally and not expensive method to degrade Orange G dye (OG) from the aqueous solution, where the extract of ficus leaves has been used to fabricate the green bimetallic iron/copper nanoparticles (G-Fe/Cu-NPs). The fabricated G‑Fe/Cu-NPs were characterized utilizing scanning electron microscopy, BET, atomic force microscopy, energy dispersive spectroscopy, Fourier-transform infrared spectroscopy and zeta potential. The rounded and shaped as like spherical nanoparticles were found for G-Fe/Cu‑NPs with the size ranged 32-59 nm and the surface area was 4.452 m²/g. Then the resultant nanoparticles were utilized as a Fenton-like oxidation catalyst. The degradation efficiency of

CdS and CdTe thin films were thermally deposited onto glass substrate. The CdCl2 layer was deposited onto CdS surface. These followed by annealing for different duration times to modify the surface and interface of the junction. The diffraction patterns showed that the intensity of the peaks increased with the CdCl2/annealed treatment, and the grain sizes are increased after CdCl2/annealed treatment

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Nonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though

Buckling and free vibration analysis of laminated rectangular plates with uniform and non uniform distributed in-plane compressive loadings along two opposite edges is performed using the Ritz method. Classical laminated plate theory is adopted. The static component of the applied in- plane loading are assumed to vary according to uniform, parabolic or linear distributions. Initially, the plate membrane problem is solved using the Ritz method; subsequently, using Hamilton’s variational principle, linear homogeneous algebraic equations in terms of unknown are generated, the set of linear algebraic equations can be solved as an Eigen-value problem. Buckling loads for laminated plates with different combinations of bounda