In this paper, a discretization of a three-dimensional fractional-order prey-predator model has been investigated with Holling type III functional response. All its fixed points are determined; also, their local stability is investigated. We extend the discretized system to an optimal control problem to get the optimal harvesting amount. For this, the discrete-time Pontryagin’s maximum principle is used. Finally, numerical simulation results are given to confirm the theoretical outputs as well as to solve the optimality problem.
Background and Objective: Public demand for procedures to rejuvenate photodamaged facial skin have stimulated the use of fractional CO2 laser as a precise and predictable treatment modality. The purpose of this study was to assess the effect of fractional CO2 laser system for reducing periorbital rhytids.
Materials and Methods: twenty seven subjects with mild periocular wrinkles, and photoaged skin of the face were prospectively treated two to three times (according to clinical response) in the periorbital area with a fractional CO2 laser device equipped with a scanning hand piece. Improvements in eyelid wrinkles was evaluated clinically and photographically. Subjects also scored satisfaction and
... Show MoreThe Caputo definition of fractional derivatives introduces solution to the difficulties appears in the numerical treatment of differential equations due its consistency in differentiating constant functions. In the same time the memory and hereditary behaviors of the time fractional order derivatives (TFODE) still common in all definitions of fractional derivatives. The use of properties of companion matrices appears in reformulating multilevel schemes as generalized two level schemes is employed with the Gerschgorin disc theorems to prove stability condition. Caputo fractional derivatives with finite difference representations is considered. Moreover the effect of using the inverse operator which tr
In This paper, we have been approximated Grűnwald-Letnikov Derivative of a function having m continuous derivatives by Bernstein Chlodowsky polynomials with proving its best approximation. As well as we have been solved Bagley-Torvik equation and Fokker–Planck equation where the derivative is in Grűnwald-Letnikov sense.
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.
This paper aims to study the fractional differential systems arising in warm plasma, which exhibits traveling wave-type solutions. Time-fractional Korteweg-De Vries (KdV) and time-fractional Kawahara equations are used to analyze cold collision-free plasma, which exhibits magnet-acoustic waves and shock wave formation respectively. The decomposition method is used to solve the proposed equations. Also, the convergence and uniqueness of the obtained solution are discussed. To illuminate the effectiveness of the presented method, the solutions of these equations are obtained and compared with the exact solution. Furthermore, solutions are obtained for different values of time-fractional order and represented graphically.
This study includes synthesis of some nitrogenous heterocyclic compounds linked to amino acid esters or heterocyclic amines that may have a potential activity as antimicrobial and/or cytotoxic. Quinolines are an important group of organic compounds that possess useful biological activity as antibacterial, antifungal and antitumor .8-Hydroxyquinoline (8-HQ) and numerous of its derivatives exhibit potent activities against fungi and bacteria which make them good candidates for the treatment of many parasitic and microbial infection diseases.
These pharmacological properties of quinolones aroused our interest in synthesizing several new compounds featuring heterocyclic rings of the quinoline derivatives linke
... Show Moreالوصف The synthesis of 2 (N-phenyl dithio carboxamid) benzothiazol Ligand (L) from reaction of 2-Mercaptobenzothiozol with phenylisothiocyanate using ratio 1: 1. The ligand was characterized by elemental analysis (CHN),'H-NMR, IR and UV-Vis. The complexes with bivalent ions (Ni, Cu, Zn, Cd and Hg) have been prepared and characterized. The structural diagnosis was established using IR, UV–Visible spectro photometer, molar conductivity, atomic absorption and molar ratio with selected metal ions (Ni2+, Cu2+). The complexes of (Ni, Cu) gave octahedral structural while the complexes of (Zn, Cd, Hg) gave tetrahedral structural. The study of biological activity of the ligand (L) and its complexes (Ni, Cu, Hg) in two deferent concentration (
... Show MoreSome azo compounds were prepared by coupling the diazonium salts of amines with 2,4-dimethylphenol The structure of azo compounds were determined on the basis of elemental analyses, 1HNMR, FT-IR and UV-Vis spectroscopic techniques. Complexes of nickel(II) and copper(II) have been synthesized and characterized. The composition of complexes has been established by using flame atomic absorption, (C.H.N) Analysis, FT-IR and UV-Vis spectroscopic methods as well as conductivity magnetic susceptibility measurements. The nature of the complexes formed were studied following the mole ratio and continuous variation methods, Beer's law obeyed over a concentration range (1×10-4 - 3×10-4 M). High molar absorbtivity of the complex solutions were observ
... Show More