A new optimal control technique for solution of HIV infection model

In this paper, by means of the optimal control technique and power series technique,we introduce a new method, namely, the optimal control power series technique, bywhich one can obtain numerical solutions of the HIV infection model of CD4+T cells.The obtained approximate solution has shown good agreement with the experimentalresults and previous simulations using other methods.https://search.hthereadinghub.com/?uc=20180302&ad=appfocus1&source=d-lp0-bb9&uid=0d8983d2-5a26-4ec4-bba5-84ea234d1896&i_id=ebooks_100.7&page=newtab&

Series Representations for Uncertain Fractional IVPs in the Fuzzy Conformable Fractional Sense

Fuzzy differential equations provide a crucial tool for modeling numerous phenomena and uncertainties that potentially arise in various applications across physics, applied sciences and engineering. Reliable and effective analytical methods are necessary to obtain the required solutions, as it is very difficult to obtain accurate solutions for certain fuzzy differential equations. In this paper, certain fuzzy approximate solutions are constructed and analyzed by means of a residual power series (RPS) technique involving some class of fuzzy fractional differential equations. The considered methodology for finding the fuzzy solutions relies on converting the target equations into two fractional crisp systems in terms of ρ-cut representations. The residual power series therefore gives solutions for the converted systems by combining fractional residual functions and fractional Taylor expansions to obtain values of the coefficients of the fractional power series. To validate the efficiency and the applicability of our proposed approach we derive solutions of the fuzzy fractional initial value problem by testing two attractive applications. The compatibility of the behavior of the solutions is determined via some graphical and numerical analysis of the proposed results. Moreover, the comparative results point out that the proposed method is more accurate compared to the other existing methods. Finally, the results attained in this article emphasize that the residual power series technique is easy, efficient, and fast for predicting solutions of the uncertain models arising in real physical phenomena.

Solution of Fractional Partial Differential Equations Using Fractional Power Series Method

In this paper, we are presenting our work where the noninteger order partial differential equation is studied analytically and numerically using the noninteger power series technique, proposed to solve a noninteger differential equation. We are familiar with a coupled system of the nonlinear partial differential equation (NLPDE). Noninteger derivatives are considered in the Caputo operator. The fractional-order power series technique for finding the nonlinear fractional-order partial differential equation is found to be relatively simple in implementation with an application of the direct power series method. We obtained the solution of nonlinear dispersive equations which are used in electromagnetic and optics signal transformation. The proposed approach of using the noninteger power series technique appears to have a good chance of lowering the computational cost of solving such problems significantly. How to paradigm an initial representation plays an important role in the subsequent process, and a few examples are provided to clarify the initial solution collection.

Conservation Laws and Exact Series Solution of Fractional-Order Hirota-Satsoma Coupled KdV system by Symmetry Analysis

In this work, we investigated the invariance analysis of fractional-order Hirota-Satsoma coupled Korteveg-de-Vries (HSC-KdV) system of equations based on Riemann-Liouville (RL) derivatives. The Lie Symmetry analysis is considered to obtain infinitesimal generators; we reduced the system of coupled equations into nonlinear fractional ordinary differential equations (FODEs) with the help of Erdelyi’s-Kober (EK) fractional differential and integral operators. The reduced system of FODEs solved by means of the power series technique with its convergence. The conservation laws of the system constructed by Noether’s theorem.

β−-Decay Half-Lives of Even-Even Nuclei Using the Recently Introduced Phase Space Recipe

In this paper, we present the β -decay half-lives calculation for selected even-even nuclei that decay through electron emission. The kinematical portion of the half-life calculation was performed using a recently introduced technique for computation of phase space factors (PSFs). The dynamical portion of our calculation was performed within the proton-neutron quasiparticle random phase approximation (pn-QRPA) model. Six nuclei ( 20 O, 24 Ne, 34 Si, 54 Ti, 62 Fe and 98 Zr) were selected for the present calculation. We compare the calculated PSFs for these cases against the traditionally used recipe. In our new approach, the Dirac equation was numerically solved by employing a Coulomb potential. This potential was adopted from a more realistic proton distribution of the daughter nucleus. Thus, the finite size of the nucleus and the diffuse nuclear surface corrections are taken into account. Moreover, a screened Coulomb potential was constructed to account for the effect of atomic screening. The power series technique was used for the numerical solution. The calculated values of half-lives, employing the recently developed method for computation of PSFs, were in good agreement with the experimental data.

Lie symmetry analysis and conservation laws for the time fractional simplified modified Kawahara equation

In this work, Lie symmetry analysis for the time fractional simplified modified Kawahara (SMK) equation with Riemann-Liouville (RL) derivative, is analyzed. We transform the time fractional SMK equation to nonlinear ordinary differential equation (ODE) of fractional order using its Lie point symmetries with a new dependent variable. In the reduced equation, the derivative is in the Erdelyi-Kober (EK) sense. We solve the reduced fractional ODE using a power series technique. Using Ibragimov’s nonlocal conservation method to time fractional partial differential equations, we compute conservation laws (Cls) for the time fractional SMK equation. Some figures of the obtained explicit solution are presented.

S1-ZGV Modes of a Linear and Nonlinear Profile for Functionally Graded Material Using Power Series Technique

The present work deals with functionally graded materials (FGM) isotropic plates in the neighborhood of the first-order symmetric zero group velocity (S1-ZGV) point. The mechanical properties of functionally graded material (FGM) are assumed to vary continuously through the thickness of the plate and obey a power law of the volume fraction of the constituents. Governing equations for the problem are derived, and the power series technique (PST) is employed to solve the recursive equations. The impact of the FGM basic materials properties on S1-ZGV frequency of FGM plate is investigated. Numerical results show that S1-ZGV frequency is comparatively more sensitive to the shear modulus. The gradient coefficient p does not affect the linear dependence of ZGV frequency fo as function of cut-off frequency fc; only the slope is slightly varied.