The motive of the study was to explore the nonlinear Riemann wave equation, which describes the tsunami and tidal waves in the sea and homogeneous and stationary media. This study establishes the framework for the analytical solutions to the Riemann wave equation using the new extended direct algebraic method. As a result, the soliton patterns of the Riemann wave equation have been successfully illustrated, with exact solutions offered by the plane solution, trigonometry solution, mixed hyperbolic solution, mixed periodic and periodic solutions, shock solution, mixed singular solution, mixed trigonometric solution, mixed shock single solution, complex soliton shock solution, singular solution, and shock wave solutions. Graphical visualization is provided of the results with suitable values of the involved parameters by Mathematica. It was visualized that the velocity of the soliton and the wave number controls the behavior of the soliton. We are confident that our research will assist physicists in predicting new notions in mathematical physics.

/pdf/explicit-soliton-structure-formation-for-the-riemann-wave-3nysv7dv.pdf

Explicit Soliton Structure Formation for the Riemann Wave Equation and a Sensitive Demonstration

Controllability results of Hilfer delay fractional derivative(HDFD) with nondense operator have been articulated in this article. Primary discussions were made on the existence of mild solution using the Banach contraction principle and continued with controllability results by Darbo-Sadavoskii fixed point theorem. Obtained results enhanced via the numerical approximation with the graphical approach. 

An interpretation on controllability of Hilfer fractional derivative with nondense domain

In this study, the explicit finite difference method is used to solve the fractional-order pseudo-hyperbolic telegraph partial differential equation by means of Caputo fractional derivative. A first-order finite difference approach is constructed for fractional order pseudo-hyperbolic telegraph partial differential equations. The difference scheme technique's stability estimate for the presented problem is given. The test problem is provided as an application. A comparison of the exact and approximate solutions is offered to determine the correctness and effectiveness of the suggested method. Finally, a graphical representation of the exact and approximate solutions in various cases is presented. The simulation of the obtained results are displayed in both the figures and the error analysis table. 

Solutions of fractional order pseudo-hyperbolic telegraph partial differential equations using finite difference method

In this study, the fractal nonlinear dispersive Boussineq-like equation is investigated by variational perspective for the first time. The fractal variational principle of the fractal Boussineq-like equation is established via fractal semi-inverse method (FSM). Based on the fractal variational principle, variational transform method (VTM) is proposed to find the exact fractal solitary wave solution for the fractal nonlinear dispersive Boussineq-like equation. The numerical examples illustrate the novel scheme is very simple and efficient. Moreover, some physical properties of fractal solitary wave solutions are illustrated by some simulation graphics. 

Fractal solitary wave solutions for fractal nonlinear dispersive boussinesq-like models

Entropy of a connected network is a quantitative measure from information theory that has triggered a plethora of research domains in molecular chemistry, biological sciences and computer programming due to its inherent capacity to explore the structural characteristics of complex molecular frameworks that have low structural symmetry as well as high diversity. The analysis of the structural order is greatly simplified through the topological indices based graph entropy metrics, which are then utilized to predict the structural features of molecular frameworks. This predictability has not only revolutionized the study of zeolitic frameworks but has also given rise to new generations of frameworks. We make a comparative study of two versatile framework topologies namely zeolites BCT and DFT, which have been widely utilized to create a new generation of frameworks known as metal organic frameworks. We discuss bond-additive topological indices and compute entropy measure descriptors for zeolites BCT and DFT using degree and degree-sum parameters. In addition, we perform bond-wise scaled comparative analysis between BCT and DFT which shows that zeolite BCT has greater entropy values compared to zeolite DFT. 

/pdf/entropy-structural-characterization-of-zeolites-bct-and-dft-25n7hb5d.pdf

Entropy structural characterization of zeolites BCT and DFT with bond-wise scaled comparison

The ongoing study deals with various forms of solutions for the biological population model with a novel beta-time derivative operators. This model is very conducive to explain the enlargement of viruses, parasites and diseases. This configuration of the aforesaid classical scheme is scouted for its new solutions especially in soliton shape via two of the well known analytical strategies, namely: the extended Sinh-Gordon equation expansion method (EShGEEM) and the Expa function method. These soliton solutions suggest that these methods have widened the scope for generating solitary waves and other solutions of fractional differential equations. Different types of soliton solutions will be gained such as dark, bright and singular solitons solutions with certain conditions. Furthermore, the obtained results can also be used in describing the biological population model in some better way. The numerical solution for the model is obtained using the finite difference method. The numerical simulations of some selected results are also given through their physical explanations. To the best of our knowledge, No previous literature discussed this model through the application of the EShGEEM and the Expa function method and supported their new obtained results by numerical analysis.

On beta-time fractional biological population model with abundant solitary wave structures

Topological indices are numerical numbers assigned to molecular graphs and are expected to predict certain of its physical or chemical properties. Metal-organic frameworks (MOFs) are inorganic/organic porous crystalline materials with a regular array of positively charged metal ions which surrounds organic linkers. Covalent organic frameworks (COFs) are a class of organic polymers with highly ordered structure and permanent porosity. In this work, we have computed some degree-based topological indices of naphthalene metal-organic frameworks and thiophene-based covalent triazine framework.

Topological Aspects of Certain Covalent Organic Frameworks and Metal Organic Frameworks

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On beta-time fractional biological population model with abundant solitary wave structures

Topological Aspects of Certain Covalent Organic Frameworks and Metal Organic Frameworks