In this paper,the homtopy perturbation method (HPM) was applied to obtain the approximate solutions of the fractional order integro-differential equations . The fractional order derivatives and fractional order integral are described in the Caputo and Riemann-Liouville sense respectively. We can easily obtain the solution from convergent the infinite series of HPM . A theorem for convergence and error estimates of the HPM for solving fractional order integro-differential equations was given. Moreover, numerical results show that our theoretical analysis are accurate and the HPM can be considered as a powerful method for solving fractional order integro-diffrential equations.
Globally, the COVID-19 pandemic’s development has presented significant societal and economic challenges. The carriers of COVID-19 transmission have also been identified as asymptomatic infected people. Yet, most epidemic models do not consider their impact when accounting for the disease’s indirect transmission. This study suggested and investigated a mathematical model replicating the spread of coronavirus disease among asymptomatic infected people. A study was conducted on every aspect of the system’s solution. The equilibrium points and the basic reproduction number were computed. The endemic equilibrium point and the disease-free equilibrium point had both undergone local stability analyses. A geometric technique was used
... Show MoreThe Ge0.4Te0.6 alloy has been prepared. Thin films of Ge0.4Te0.6 has been prepared via a thermal evaporation method with 4000A thickness, and rate of deposition (4.2) A/sec at pressure 2x10-6 Torr. The A.C electrical conductivity of a-Ge0.4Te0.6 thin films has been studied as a function of frequency for annealing temperature within the range (423-623) K, the deduced exponent s values, was found to decrease with increasing of annealing temperature through the frequency of the range (102-106) Hz. It was found that, the correlated barrier hopping (CBH) is the dominant conduction mechanism. Values of dielectric constant ε1 and dielectric loss ε2 were found to decrease with frequency and increase with temperature. The activation energies have
... Show MoreIn this paper, we investigate the behavior of the bayes estimators, for the scale parameter of the Gompertz distribution under two different loss functions such as, the squared error loss function, the exponential loss function (proposed), based different double prior distributions represented as erlang with inverse levy prior, erlang with non-informative prior, inverse levy with non-informative prior and erlang with chi-square prior.
The simulation method was fulfilled to obtain the results, including the estimated values and the mean square error (MSE) for the scale parameter of the Gompertz distribution, for different cases for the scale parameter of the Gompertz distr
... Show MoreTopological indices provide important insights into the structural characteristics of molecular graphs. The present investigation proposes and explores a creative graph on a finite group G, which is known as the RIG. This graph is designated as ΓRS G2(4) indicating a simple undirected graph containing elements of G. Two distinct ertices are regarded as nearly the same if and only if their sum yields a non-trivial involution element in G. RIGs have been discovered in various finite groups. We examine several facets of the RIG by altering the graph through the conjugacy classes of G. Furthermore, we investigate the topological indices as applications in graph theory applying the distance matrix of the G2(4) group.
Tobacco products of all kinds are harmful to public health, so legislation has paid great attention to regulating the process of tobacco production and distribution, whether at the level of national or international legislation, in a way that achieves legal protection for these products, so the establishment of civil liability for tobacco companies as a result of harm to the smoker The positive and the negative provoked a jurisprudential dispute due to the specificity of the work of these companies, and the jurisprudence differed in the legal nature of tobacco companies ’liability between contractual and tort liability in a way that enables the injured smoker to obtain his right to compensation.
Background: Mondor's disease means superficial thrombophlibitis of the chest wall in human, treatment is entirely symptomatic. Hot, wet dressing and anodynes may be used for pain relief.
Objective: To evaluate the role of systemic and transdermal action of diclofenac (olfen) with respect to the symptom and sign (pain, erythema along the superficial vein), and the use of Doppler ultrasonography which is a colored ultrasound used for assessment of flow of blood in vessels.
Method: The study was performed on 12 cases with Mondor's disease in middle age female patients with the involvement of lnframammary veins in all of the them (commonly affected), 4 cases had reassurance only, 4 cases had reassurance with systemic diclofenac, and th