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This work employs the Extended Direct Algebraic Method (EDAM) to solve quadratic and cubic nonlinear Klein–Gordon Equations (KGEs), which are standard models in particle and quantum physics that describe the dynamics of scaler particles with spin zero in the framework of Einstein’s theory of relativity. By applying variables-based wave transformations, the targeted KGEs are converted into Nonlinear Ordinary Differential Equations (NODEs). The resultant NODEs are subsequently reduced to a set of nonlinear algebraic equations through the assumption of series-based solutions for them. New families of soliton solutions are obtained in the form of hyperbolic, trigonometric, exponential and rational functions when these systems are solved using Maple. A few soliton solutions are considered for certain values of the given parameters with the help of contour and 3D plots, which indicate that the solitons exist in the form of dark kink, hump kink, lump-like kink, bright kink and cuspon kink solitons. These soliton solutions are relevant to actual physics, for instance, in the context of particle physics and theories of quantum fields. These solutions are useful also for the enhancement of our understanding of the basic particle interactions and wave dynamics at all levels of physics, including but not limited to cosmology, compact matter physics and nonlinear optics.

In the present research work, we construct and examine the self-similarity of optical solitons by employing the Riccati Modified Extended Simple Equation Method (RMESEM) within the framework of non-integrable Coupled Nonlinear Helmholtz Equations (CNHEs). This system models the transmission of optical solitons and coupled wave packets in nonlinear optical fibers and describes transverse effects in nonlinear fiber optics. Initially, a complex transformation is used to convert the model into a single Nonlinear Ordinary Differential Equation (NODE), from which hyperbolic, exponential, rational, trigonometric, and rational hyperbolic solutions are produced. In order to better understand the physical dynamics, we offer several 3D, contour, and 2D illustrations for the independent selections of physical parameter values. These illustrations highlight the graphic behaviour of some optical solitons and demonstrate that, under certain constraint conditions, acquired optical solitons lose their stability when they approach an axis and display periodic-axial perturbations, which lead to the generation of optical fractals. As a framework, the generated optical solitons have several useful applications in the field of telecommunications. Furthermore, our suggested RMESEM demonstrates its use by broadening the spectrum of optical soliton solutions, offering important insights into the dynamics of the CNHEs, and suggesting possible applications in the management of nonlinear models.

The dynamical wave solutions of the time–space fractional Date–Jimbo–Kashiwara–Miwa (DJKM) equation have been obtained in this article using an innovative and efficient technique including the Riccati–Bernoulli sub-ODE method through Bäcklund transformation. Fractional-order derivatives enter into play for their novel contribution to the enhancement of the characterization of dynamic waves while providing better modeling ability compared to integer types of derivatives. The solutions of the above-mentioned time–space fractional Date–Jimbo–Kashiwara–Miwa equation have tremendous importance in numerous scientific scenarios. The regular dynamical wave solutions of the aforementioned equation encompass three fundamental functions: trigonometric, hyperbolic, and rational functions will be among the topics covered. These solutions are graphically classified into three categories: compacton kink solitary wave solutions, kink soliton wave solutions and anti-kink soliton wave solutions. In addition, to explore the impact of the fractional parameter (α) on those solutions, 2D plots are utilized, while 3D plots are applied to present the solutions involving the integer-order derivatives.

In this article, we construct sufficient conditions that secure the non-emptiness and compactness of the set of antiperiodic solutions of an impulsive fractional differential inclusion involving an ω-weighted ϱ–Hilfer fractional derivative, D0,tσ,v,ϱ,ω, of order σ∈(1,2), in infinite-dimensional Banach spaces. First, we deduce the formula of antiperiodic solutions for the observed problem. Then, we give two theorems regarding the existence of these solutions. In the first, by using a fixed-point theorem for condensing multivalued functions, we show the non-emptiness and compactness of the set of antiperiodic solutions; and in the second, by applying a fixed-point theorem for contraction multivalued functions, we prove the non-emptiness of this set. Because many types of famous fractional differential operators are particular cases from the operator D0,tσ,v,ϱ,ω, our results generalize several recent results. Moreover, there are no previous studies on antiperiodic solutions for this type of fractional differential inclusion, so this work is novel and interesting. We provide two examples to illustrate and support our conclusions.

The aim of this work is to obtain novel and interesting results for mild solutions to a semilinear differential inclusion involving a w-weighted, Φ-Hilfer, fractional derivative of order μ∈(1,2) with non-instantaneous impulses in Banach spaces with infinite dimensions when the linear term is the infinitesimal generator of a strongly continuous cosine family and the nonlinear term is a multi-valued function. First, we determine the formula of the mild solution function for the considered semilinear differential inclusion. Then, we give sufficient conditions to ensure that the mild solution set is not empty or compact. The desired results are achieved by using the properties of both the w-weighted Φ-Laplace transform, w-weighted ψ-convolution and the measure of non-compactness. Since the operator, the w-weighted Φ-Hilfer, includes well-known types of fractional differential operators, our results generalize several recent results in the literature. Moreover, our results are novel because no one has previously studied these types of semilinear differential inclusions. Finally, we give an illustrative example that supports our theoretical results.

The Zoomeron equation plays a significant role in many fields of physics, especially in soliton theory, such as helping to reveal new distinctive properties in different physical phenomena such as fluid dynamics, laser physics, and nonlinear optics. By using the Riccati–Bernoulli sub-ODE approach and the Backlund transformation, we search for soliton solutions of the fractional Zoomeron nonlinear equation. A number of solutions have been put forth, such as kink, anti-kink, cuspon kink, lump-type kink solitons, single solitons, and others defined in terms of pseudo almost periodic functions. The (2 + 1)-dimensional fractional Zoomeron equation given in a form undergoes precise dynamics. We use the computational software, Matlab 19, to express these solutions graphically by changing the value of various parameters involved. A detailed analysis of their dynamics allows us to obtain completely better insights necessarily with the elementary physical phenomena controlled by the fractional Zoomeron equation.

This study introduces two innovative methods, the new transform iteration method and the residual power series transform method, to solve fractional nonlinear system Korteweg–de Vries (KdV) equations. These equations, fundamental in describing nonlinear wave phenomena, present complexities due to the involvement of fractional derivatives. In demonstrating the application of the new transform iteration method and the residual power series transform method, computational analyses showcase their efficiency and accuracy in computing solutions for fractional nonlinear system KdV equations. Tables and figures accompanying this research present the obtained solutions, highlighting the superior performance of the new transform iteration method and the residual power series transform method compared to existing methods. The results underscore the efficacy of these novel methods in handling complex nonlinear equations involving fractional derivatives, suggesting their potential for broader applicability in similar mathematical problems.

The primary goal of this study is to create and characterise solitary wave solutions for the conformable Fractional Coupled Boussinesq-Whitham-Broer-Kaup Equations (FCBWBKEs), a model that governs shallow water waves. Through wave transformations and the chain rule, the authors used the modified Extended Direct Algebraic Method (mEDAM) for transforming FCBWBKEs into a more manageable Nonlinear Ordinary Differential Equation (NODE). This accomplishment is particularly noteworthy because it surpasses the drawbacks linked to both the Caputo and Riemann–Liouville definitions in complying to the chain rule. The study uses visual representations such as 3D, 2D, and contour graphs to demonstrate the dynamic nature of solitary wave solutions. Furthermore, the investigation of diverse wave phenomena such as kinks, shock waves, periodic waves, and bell-shaped kink waves highlights the range of knowledge obtained in the study of shallow water wave behavior. Overall, this study introduces novel methodologies that produce valuable and consistent results for the problem under consideration.

In this paper, we introduce and implement the optimal auxiliary function method to solve a system of fractional-order Whitham–Broer–Kaup equations, a class of nonlinear partial differential equations with broad applications in mathematical physics. This method provides a systematic and efficient approach to finding accurate solutions for complex systems of fractional-order equations. We give a full analysis using tables and figures to demonstrate the reliability and accuracy of our approach. We confirm the effectiveness of our suggested method in solving the considered equations using numerical simulations and comparisons, emphasizing its potential for applications in a variety of scientific and engineering areas.

This work investigates the complex dynamics of the stochastic fractional Kuramoto–Sivashinsky equation (SFKSE) with conformable fractional derivatives. The research begins with the creation of singular stochastic soliton solutions utilizing the modified extended direct algebraic method (mEDAM). Comprehensive contour, 3D, and 2D visual representations clearly depict the categorization of these stochastic soliton solutions as kink waves or shock waves, offering a clear description of these soliton behaviors within the context of the SFKSE framework. The paper also illustrates the flexibility of the transformation-based approach mEDAM for investigating soliton occurrence not only in SFKSE but also in a wide range of nonlinear fractional partial differential equations (FPDEs). Furthermore, the analysis considers the effect of noise, specifically Brownian motion, on soliton solutions and wave dynamics, revealing the significant influence of randomness on the propagation, generation, and stability of soliton in complex stochastic systems and advancing our understanding of extreme behaviors in scientific and engineering domains.

In this paper, we study the numerical solution of fractional Jaulent–Miodek equations with the help of two modified methods: coupled fractional variational iteration transformation technique and the Adomian decomposition transformation technique. The Jaulent–Miodek equation has applications in several related fields of physics, including control theory of dynamical systems, anomalous transport, image and signal processing, financial modelings, nanotechnology, viscoelasticity, nanoprecipitate growth in solid solutions, random walk, modeling for shape memory polymers, condensed matter physics, fluid mechanics, optics and plasma physics. The results are presented as a series of quickly converging solutions. Analytical solutions have been performed in absolute error to confirm the proposed methodologies are trustworthy and accurate. The generated solutions are visually illustrated to guarantee the validity and applicability of the taken into consideration algorithm. The study’s findings show that, compared to alternative analytical approaches for analyzing fractional non-linear coupled Jaulent–Miodek equations, the Adomian decomposition transform method and the variational iteration transform method are computationally very efficient and accurate.

In this paper, we study a fractional Brusselator reaction–diffusion model with the help of the residual power series transform method. Specific reaction–diffusion chemical processes are modeled by applying the fractional Brusselator reaction–diffusion model. It should be mentioned that many problems in nonlinear science are characterized by fractional differential equations, where an unknown term occurs when a fractional-order derivative is operating on it. The analytic method of this problem is rarely discussed in the literature, despite numerous scholars having researched its application and usefulness. To validate our proposed method’s accuracy, we compare the numerical results of the residual power series transform method and the exact result with different fractional orders. The solution shows that the introduced approach is a good tool for solving linear and nonlinear fractional system differential equations. Finally, we provide two and three-dimensional graphical plots to support the impact of the fractional derivative on the behavior of the achieved profile results to the proposed equations.

In this paper, fractional-order system gas dynamics equations are solved analytically using an appealing novel method known as the Laplace residual power series technique, which is based on the coupling of the residual power series approach with the Laplace transform operator to develop analytical and approximate solutions in quick convergent series types by utilizing the idea of the limit with less effort and time than the residual power series method. The given model is tested and simulated to confirm the proposed technique’s simplicity, performance, and viability. The results show that the above-mentioned technique is simple, reliable, and appropriate for investigating nonlinear engineering and physical problems.

The genus capripoxvirus (CaPV), family Poxviridae, includes three virus species: goatpox virus (GPV), sheeppox virus (SPV) and lumpy skin disease virus (LSDV). CaPV causes disease outbreaks with consequent economic losses in Africa and the Middle East. LSDV has recently spread to Southeast Europe. As CaPVs share 96–97% genetic similarity along the length of the entire genome and are difficult to distinguish using serological assays, simple, reliable and fast methods for diagnosis and species differentiation are crucial in cases of disease outbreak. The present study aimed to develop a field-applicable CaPV differentiation method. Nanopore technology was used for whole genome sequencing. A local database of complete CaPV genomes and partial sequences of three genes (RPO30, P32 and GPCR) was established for offline Basic Local Alignment Search Tool (BLAST). Specificities of 98.04% in whole genome and 97.86% in RPO30 gene runs were obtained among the three virus species, while other databases were less specific. The total run time was shortened to approximately 2 h. Functionality of the developed procedure was proved by samples with high host background sequences. Reliable differentiation options for the quality and capacity of hardware, and sample quality of suspected cases, were derived from these findings. The whole workflow can be performed rapidly with a mobile suitcase laboratory and mini-computer, allowing application at the point-of-need with limited resource settings.

This article proposes a new fractional-order discrete-time chaotic system, without equilibria, included two quadratic nonlinearities terms. The dynamics of this system were experimentally investigated via bifurcation diagrams and largest Lyapunov exponent. Besides, some chaotic tests such as the 0–1 test and approximate entropy (ApEn) were included to detect the performance of our numerical results. Furthermore, a valid control method of stabilization is introduced to regulate the proposed system in such a way as to force all its states to adaptively tend toward the equilibrium point at zero. All theoretical findings in this work have been verified numerically using MATLAB software package.

Background and Aims: SARS-CoV-2-infected patients can experience long-lasting symptoms even after the resolution of the acute infection. This condition, defined as Long COVID, is now recognized as a public health priority and its negative impact on the quality of life of the patients could be more relevant in individuals with debilitating pathologies. We here evaluated the frequency of Long COVID in patients with inflammatory bowel diseases (IBD)., Methods: IBD patients afferent for scheduled visits to our tertiary referral center at the Tor Vergata University Hospital, Rome, were recruited from 7 September to 22 October 2021. During the visits, patients were investigated about previous COVID-19 infection and the possible development of Long COVID., Results: Fifty-three out of 528 IBD patients (10%) have had a SARS-CoV-2 infection. Of these, 21 patients (40%) developed Long COVID, and asthenia was the more frequent symptom as it occurred in nearly two-thirds of patients. Patients with Long COVID were more frequently females, while other clinical and demographic characteristics did not differ between patients with Long COVID and those without Long COVID. In particular, the IBD relapses occurred with the same frequency in the two groups., Conclusions: Long COVID appears to be common in IBD patients even though it does not influence the IBD course.