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In this paper, we investigate the optical solitons of the fractional complex Ginzburg–Landau equation (CGLE) with Kerr law nonlinearity which shows various phenomena in physics like nonlinear waves, second-order phase transition, superconductivity, superfluidity, liquid crystals, and strings in field theory. A comparative approach is practised between the three suggested definitions of derivative viz. conformable, beta, and M-truncated. We have constructed the optical solitons of the considered model with a new extended direct algebraic scheme. By utilization of this technique, obtained solutions carry a variety of new families including dark-bright, dark, dark-singular, and singular solutions of Type 1 and 2, and sufficient conditions for the existence of these structures are given. Further, graphical representations of the obtained solutions are depicted. A detailed comparison of solutions to the considered problem, obtained by using different definitions of derivatives, is reported as well.

Information theory is used in many branches of science and technology. For instance, to inform a set of human beings living in a particular region about the fatality of a disease, one makes use of existing information and then converts it into a mathematical equation for prediction. In this work, a model of the well-known river blindness disease is created via the Caputo and beta derivatives. A partial study of stability analysis was presented. The extended system describing the spread of this disease was solved via two analytical techniques: the Laplace perturbation and the homotopy decomposition methods. Summaries of the iteration methods used were provided to derive special solutions to the extended systems. Employing some theoretical parameters, we present some numerical simulations.

This study introduces an integrable generalization of the Kadomtsev–Petviashvili model in arbitrary spatial dimensions. The Kadomtsev–Petviashvili equation serves as a fundamental framework in describing a wide range of physical phenomena, including hydrodynamic wave disturbances, plasma dynamics, and nonlinear optical systems. In this work, the classical Kadomtsev–Petviashvili equation is modified to incorporate -fractional derivatives, extending its applicability to more complex dynamical scenarios. By employing the extended tanh function method in conjunction with the Riccati differential equation, an analytical of exact solutions such as dark, singular, and periodic wave forms are derived. These solutions give valuable mathematical insight into wave propagation and offer significant physical relevance for practical applications in physics and engineering. Two-dimensional (2D) and three-dimensional (3D) plots of the obtained wave equations are drawn under certain values of the parameters and at different cases of . In order to investigate further the system’s dynamical properties, the governing equations were transformed by means of the Galilean transformation. That way, a detailed investigation of the nonlinear structure was possible. A phase space analysis is carried out using planar dynamical system techniques in order to find bifurcations, chaotic behavior, and sensitivity of the system to initial conditions. An instability analysis due to the interaction of nonlinear and dispersive effects in the proposed model is carried out. The stability criterion for waves with regard to small perturbations was determined. Our results are contrary to the findings available in the literature, and this is the first attempt that has been made to study the Hamiltonian structure, bifurcation analysis, sensitivity analysis, and modulation instability for the model considered.

Intravenous idarucizumab, an antibody fragment of a human antibody specific for dabigatran, produced rapid reversal of the anticoagulant effect in patients with bleeding or an urgent surgical indication with no apparent toxic effects or rebound hypercoagulable state. A non–vitamin K antagonist oral anticoagulant, dabigatran etexilate (dabigatran) is an oral thrombin inhibitor that is licensed for the prevention of stroke in patients with nonvalvular atrial fibrillation and for the prevention and treatment of venous thromboembolism. Although dabigatran is associated with less serious bleeding than warfarin, 1 – 3 life-threatening bleeding can occur; in addition, dabigatran-treated patients may require urgent surgery or intervention, and dabigatran can increase the risk of perioperative bleeding. To improve the treatment of such patients, a specific dabigatran-reversal agent would be beneficial. Idarucizumab, a monoclonal antibody fragment, binds dabigatran with an affinity that is 350 times as . . .

This study introduces an integrable generalization of the Kadomtsev–Petviashvili model in arbitrary spatial dimensions. The Kadomtsev–Petviashvili equation serves as a fundamental framework in describing a wide range of physical phenomena, including hydrodynamic wave disturbances, plasma dynamics, and nonlinear optical systems. In this work, the classical Kadomtsev–Petviashvili equation is modified to incorporate -fractional derivatives, extending its applicability to more complex dynamical scenarios. By employing the extended tanh function method in conjunction with the Riccati differential equation, an analytical of exact solutions such as dark, singular, and periodic wave forms are derived. These solutions give valuable mathematical insight into wave propagation and offer significant physical relevance for practical applications in physics and engineering. Two-dimensional (2D) and three-dimensional (3D) plots of the obtained wave equations are drawn under certain values of the parameters and at different cases of . In order to investigate further the system’s dynamical properties, the governing equations were transformed by means of the Galilean transformation. That way, a detailed investigation of the nonlinear structure was possible. A phase space analysis is carried out using planar dynamical system techniques in order to find bifurcations, chaotic behavior, and sensitivity of the system to initial conditions. An instability analysis due to the interaction of nonlinear and dispersive effects in the proposed model is carried out. The stability criterion for waves with regard to small perturbations was determined. Our results are contrary to the findings available in the literature, and this is the first attempt that has been made to study the Hamiltonian structure, bifurcation analysis, sensitivity analysis, and modulation instability for the model considered.

The major goal of the current research is to investigate the effects of fractional parameters on the dynamic response of soliton waves of fractional non-linear density-dependent reaction diffusion equation. Two well-known integration methodologies: the advanced exp ( - Θ ( ξ ) ) -expansion method and the modified auxiliary equation method in the sense of beta derivative and M -fractional derivative have been implemented to achieve explicit solitonic solutions of the fractional non-linear density-dependent reaction diffusion equation that emerged in mathematical biology. The spatial dynamics of populations, chemical concentrations, or other quantities are commonly studied using this equation type in biology, ecology, and chemistry. Solitary wave solutions of the governing equation, representing the dynamics of waves, plays a vital rule in many branches of biology, ecology, and chemistry. The obtained solutions has been studied in the form of singular kink-type solitary wave and kink-wave solutions. The behavior of soliton wave solutions is also demonstrated via 2D and 3D graphs. As a result of the fractional effects, physical changes are observed. The acquired results manifest that the proposed methods are more convenient, adequate, powerful and efficacious than other direct analytical methods. The attained results might improve our understanding of how waves propagate and could benefit the fields of medicine and allied sciences.

In this article, we develop a unified framework for studying some derivatives defined as limits. This framework, the -derivative, is used to investigate the relationships between these derivatives and their relation to the ordinary derivative. It is shown that the existence of any of these derivatives is equivalent to the existence of the ordinary derivative. By using these results, we show that two derivatives that appear in the literature under different names are actually identical, and an infinite family of derivatives actually consists of only one member. We also give a unified form for the integral corresponding to these derivatives, generalize the standard analysis theorems to this setting, and relate our results to those of other researchers. Finally, we address the question of whether these derivatives should be considered fractional derivatives.

Patients with venous thromboembolism who had received initial anticoagulant therapy were studied in two trials of dabigatran. Dabigatran was effective in preventing recurrent venous thromboembolism and carried a lower risk of bleeding than warfarin but a higher risk than placebo. Anticoagulant treatment with vitamin K antagonists is recommended for patients with venous thromboembolism. 1 Most patients receive at least 3 months of treatment. Long-term treatment is recommended if there are risk factors for recurrence, such as multiple thrombotic episodes. 1 In the absence of clear contraindications to anticoagulant therapy, the risk of major bleeding is approximately 1% per year with extended vitamin K antagonist therapy after venous thromboembolism. 2 The risk of major bleeding, together with the need for frequent laboratory monitoring and dose adjustments, makes long-term treatment problematic. Dabigatran, a direct thrombin inhibitor, does not require frequent monitoring and dose adjustments. At . . .

In this study, the Jacobi elliptic function method (JEFM) and modified auxiliary equation method (MAEM) are used to investigate the solitary wave solutions of the nonlinear coupled Riemann wave (RW) equation. Nonlinear coupled partial differential equations (NLPDEs) can be transformed into a collection of algebraic equations by utilising a travelling wave transformation. This study’s objective is to learn more about the non-linear coupled RW equation, which accounts for tidal waves, tsunamis, and static uniform media. The variance in the governing model’s travelling wave behavior is investigated using the conformable, beta, and M-truncated derivatives (M-TD). The aforementioned methods can be used to derive solitary wave solutions for trigonometric, hyperbolic, and jacobi functions. We may produce periodic solutions, bell-form soliton, anti-bell-shape soliton, M-shaped, and W-shaped solitons by altering specific parameter values. The mathematical form of each pair of travelling wave solutions is symmetric. Lastly, in order to emphasise the impact of conformable, beta, and M-TD on the behaviour and symmetric solutions for the presented problem, the 2D and 3D representations of the analytical soliton solutions can be produced using Mathematica 10.

In a phase 2 trial, patients with mechanical heart valves were randomly assigned to receive either dabigatran or warfarin for anticoagulation. Dabigatran was associated with higher rates of ischemic stroke (5%, vs. 0% with warfarin) and major bleeding (4% vs. 2%). Prosthetic heart-valve replacement is recommended for many patients with severe valvular heart disease and is performed in several hundred thousand patients worldwide each year. 1 Mechanical valves are more durable than bioprosthetic valves 2 but typically require lifelong anticoagulant therapy. The use of vitamin K antagonists provides excellent protection against thromboembolic complications in patients with mechanical heart valves 3 but requires restrictions on food, alcohol, and drugs and lifelong coagulation monitoring. Because of the limitations of vitamin K antagonists, many patients opt for a bioprosthesis rather than a mechanical valve, despite the higher risk of premature valve failure requiring repeat valve-replacement surgery with . . .