Solution approximations for a mathematical model of relativistic electrons with beta derivative

The main aim of this paper is to obtain the exact and semi-analytical solutions of the nonlinear Klein-Fock-Gordon(KFG)equation which is a model of relativistic electrons arising in the laser thermonuclear fusion with beta derivative.For this purpose,both the modified extended tanh-function(mETF)method and the homotopy analysis method(HAM)are used.While applying the mETF the chain rule for beta derivative and complex wave transform are used for obtaining the exact solution.The advantage of this procedure is that discretization or normalization is not required.By applying the mETF,the exact solutions are obtained.Also,by applying the HAM semi-analytical results for the considered equation are acquired.In HAM?curve gives us a chance to find the suitable value of the for the convergence of the solution series.Also,comparative graphical representations are given to show the effectiveness,reliability of the methods.The results show that the m ETF and HAM are reliable and applicable tools for obtaining the solutions of non-linear fractional partial differential equations that involve beta derivative.This study can bring a new perspective for studies on fractional differential equations.On the other hand,it can be said that scientists can apply the considered methods for different mathematical models arising in physics,chemistry,engineering,social sciences and etc.which involves fractional differentiation.Briefly the results may cause a new insight who studies on relativistic electron modelling.

New Wave Solutions of Time-Fractional Coupled Boussinesq–Whitham–Broer–Kaup Equation as A Model of Water Waves

The main purpose of this paper is to obtain the wave solutions of conformable time fractional Boussinesq–Whitham–Broer–Kaup equation arising as a model of shallow water waves. For this aim, the authors employed auxiliary equation method which is based on a nonlinear ordinary differential equation. By using conformable wave transform and chain rule, a nonlinear fractional partial differential equation is converted to a nonlinear ordinary differential equation. This is a significant impact because neither Caputo definition nor Riemann–Liouville definition satisfies the chain rule. While the exact solutions of the fractional partial derivatives cannot be obtained due to the existing drawbacks of Caputo or Riemann–Liouville definitions, the reliable solutions can be achieved for the equations defined by conformable fractional derivatives.

Alteration of sister chromatid exchange frequencies in gastric cancer and chronic atrophic gastritis patients with and without H pylori infection

AIM: To determine, by counting sister chromatid exchange (SCE) frequencies, whether genetic impairment and DNA damage have an effect on the pathogenesis of gastric cancer (GC). METHODS: Analysis of SCE is a cytogenetic technique used to show DNA damage as a result of an exchange of DNA fragments between sister chromatids. We analyzed SCE frequency in 24 patients with GC, 26 patients with chronic atrophic gastritis (CAG), and 15 normal controls. The presence of H pylori was confirmed by urease test, toluidine-blue stain and hematoxylin-eosin stain. RESULTS: SCE was significantly increased in H pylori- negative GC patients, and in H pylori-negative CAG patients compared with controls (7.41 ± 1.36 and 6.92 ± 1.20, respectively, vs 5.54 ± 0.8, P < 0.001). There was no difference in the SCE frequency between H pylori- negative GC patients and H pylori-negative CAG patients (P > 0.05). On other hand, the SCE frequencies in H pylori-positive GC patients were higher than those in H pylori-positive CAG patients (9.20 ± 0.94 vs 7.93 ± 0.81, P < 0.01). Furthermore, H pylori-positive GC patients had a higher SCE frequency than H pylori- negative GC patients (9.20 ± 0.94 vs 7.41 ± 1.36, P < 0.001). Similarly, a significant difference was detected between H pylori-positive CAG patients and H pylori-negative CAG patients (7.93 ± 0.81 vs 6.92 ± 1.20, P < 0.05). CONCLUSION: We suggest the increased SCE in patients reflects a genomic instability that may be operative in gastric carcinogenesis.

New Analytical and Numerical Results For Fractional Bogoyavlensky-Konopelchenko Equation Arising in Fluid Dynamics

In this article,(2+1)-dimensional time fractional Bogoyavlensky-Konopelchenko(BK)equation is studied,which describes the interaction of wave propagating along the x axis and y axis.To acquire the exact solutions of BK equation we employed sub equation method that is predicated on Riccati equation,and for numerical solutions the residual power series method is implemented.Some graphical results that compares the numerical and analytical solutions are given for di erent values of.Also comparative table for the obtained solutions is presented.

Relationship between pinguecula formation and exposure to tandoor ovens in a hospital-based study

AIM: To investigate the relationship between pinguecula and the use of tandoor ovens.METHODS: A total of 539 women, ranging in age from20 to 86 y who attended an outpatient clinic were enrolled. All the patients were asked whether they used tandoor ovens. Women exposed to tandoor ovens(n =286) were accepted as participants in the study group and they were compared with participants in the control group(n =253). The age, presence of pinguecula,duration of exposure to tandoor ovens as years and occupations were recorded for all the subjects.RESULTS: Mean duration for exposure to tandoor was20.26y(range 1-62y) in the study group. The rate of pinguecula in the study group was 82.2%(235/286), and the rate in the control group was 37.5%(95/253); this difference was statistically significant(P 【0.05).Pinguecula was seen in 61.2%(330/539) of all the participants.CONCLUSION: Pinguecula is strongly associated with exposure to tandoor ovens.

Two effective approaches for solving fractional generalized Hirota-Satsuma coupled KdV system arising in interaction of long waves

In this article,two different methods,namely sub-equation method and residual power series method,have been used to obtain new exact and approximate solutions of the generalized Hirota-Satsuma system of equations,which is a coupled KdV model.The fractional derivative is taken in the conformable sense.Each of the obtained exact solutions were checked by substituting them into the corresponding system with the help of Maple symbolic computation package.The results indicate that both methods are easy to implement,effective and reliable.They are therefore ready to apply for various partial fractional differential equations.

Multiple-solitons for generalized(2+1)-dimensional conformable Korteweg-de Vries-Kadomtsev-Petviashvili equation

This paper studied new class of integral equation called the Korteweg-de Vries-Kadomtsev-Petviashvili(KdV-KP)equation.This equation consist of the well-known fifth-order KdV equation in the context of the Kadomtsev-Petviashvili equation.The newly gathered class of sixth-order KdV-KP equation is studied using the sub-equation method to obtain several soliton-type solutions which consist of trigonometric,hyperbolic,and rational solutions.The application of the sub-equation approach in this work draws attention to the outstanding characteristics of the suggested method and its ability to handle completely integrable equations.Furthermore,the obtained solutions have not been reported in the previous literature and might have significant impact on future research.

Soliton solutions for time fractional ocean engineering models with Beta derivative

In this study,the authors obtained the soliton and periodic wave solutions for time fractional symmetric regularized long wave equation(SRLW)and Ostrovsky equation(OE)both arising as a model in ocean engineering.For this aim modified extended tanh-function(mETF)is used.While using this method,chain rule is employed to turn fractional nonlinear partial differential equation into the nonlinear ordinary differential equation in integer order.Owing to the chain rule,there is no further requirement for any normalization or discretization.Beta derivative which involves fractional term is used in considered mathematical models.Obtaining the exact solutions of these equations is very important for knowing the wave behavior in ocean engineering models.