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Nematicons upgrade the recognition of light localization in the reorientation of non-local media. the current research employs a powerful integral scheme using a different procedure, namely, the modified simple equation method (MSEM), to analyze nematicons in liquid crystals from the controlling model. The expanded MSEM is investigated to enlarge the applicability of the standard one. The suggested expansion depends on merging the MSEM and the ansatz method. The new generalized nonlinear n-times quadruple power law is included. With the aid of the symbolic computational package Mathematica, new explicit complex hyperbolic, periodic, and more exact spatial soliton solutions are derived. Moreover, the related existence constraints are obtained. To show the dynamical properties of some of the obtained nematicons, three-dimensional profiles with corresponding contours are depicted with the choice of appropriate values of arbitrary parameters. The fractional impacts in various applicable senses are analyzed to investigate the generality of the considered model.

Purpose: The physical dynamic and impact of many problems is successfully attributed via fractional approach. The fractional models more effectively present the insight of many problems which maintain the memory effects. Owing to excellent thermal activities and alters, the nanoparticles are more superior contrasting to base liquids. Different dynamic of nanoparticles are reported in the heating transmission systems, engineering processes and industrial framework. Design/methodology/approach: Present study elucidates the heat transfer distribution in Oldroyd-B nanofluid which is decomposition of copper nanoparticles with blood base fluid. The variable thermal conductivity function is assumed to treat the nanofluid problem. Furthermore, the viscous dissipation consequences are utilized in order to modifying the problem. The modeling is based on Caputo fractional forms. The finite difference simulations are performed to computing the numerical results. Thermal results for nanofluid model are physical claimed with variation of flow parameters 0≤Ha≤5,1≤Gr≤3,0.01≤φ≤0.2,0≤ϵ≤1,0≤Ec≤1 and α=β∈(0,1].. Findings: The claimed results verify that boosted thermal phenomenon is associated under the variable thermal conductivity assumptions. The increasing volume fractional parameter role is noted for temperature profile. The heat transfer pattern is increasing function of nanoparticles volume fraction while controlling results are noted for fractional parameter. Based on reported results, it is claimed that current solution approach can be further implemented to different physical problems.

In this paper, an innovative mathematical approach is adopted to construct new formulation for exploring thermal characteristics in Jeffery Hamel flow between non-parallel convergent-divergent channels using non-Fourier's law. Due to the occurrence of isothermal flow of non-Newtonian fluids through non-uniform surfaces in many industrial and technological processes, such as film condensation, plastic sheet deformation, crystallization, cooling of metallic sheets, design of nozzles devices, supersonic and various heat exchangers, and glass and polymer industries, the current research is focused on this topic. To modulate this flow, the flow stream is subjected in a non-uniform channel. By incorporating relaxations in Fourier's law, thermal and concentration flux intensities are examined. In the process of mathematically simulating the flow problem, we constructed a set of governing partial differential equations that were embedded with a variety of various parameters. These equations are simplified into order differential equations using the vogue variable conversion approach. By selecting the default tolerance, the MATLAB solver bvp4c completes the numerical simulation. The temperature and concentration profiles were determined to be affected in opposing ways by thermal and concentration relaxations, while thermophoresis improved both fluxes. Inertial forces in a convergent channel accelerate the fluid in a convergent channel, while in the divergent channel the stream is shrink. The temperature distribution of Fourier's law is stronger than that of the non-Fourier's heat flux model. The study has real-world significance in the food business and is pertinent to energy systems, biomedical technology, and contemporary aircraft systems.

In this dissertation, we study the coupled system of q$$ q $$‐fractional Langevin differential equations involving q$$ q $$‐Caputo derivative having q$$ q $$‐fractional integral conditions. With the help of some adequate conditions, we investigate the uniqueness and existence of mild solution of the aforementioned system. We also analyze various kinds of Ulam's stability. Banach fixed point theorem and Leray–Schauder of cone type are used to illustrate the existence and uniqueness results. We also used non‐linear functional analysis methods to explore variety of stability types. An example is provided to clearly demonstrate our theoretical outcomes. [ABSTRACT FROM AUTHOR]

Roads can be significant traffic lifelines that can be damaged by collapsed tree branches, landslide rubble, and buildings debris. Thus, road damage detection and evaluation by utilizing High-Resolution Remote Sensing Images (RSI) are highly important to maintain routes in optimal conditions and execute rescue operations. Detecting damaged road areas through high-resolution aerial images could promote faster and effectual disaster management and decision making. Several techniques for the prediction and detection of road damage caused by earthquakes are available. Recently, computer vision (CV) techniques have appeared as an optimal solution for road damage automated inspection. This article presents a new Road Damage Detection modality using the Hunger Games Search with Elman Neural Network (RDD–HGSENN) on High-Resolution RSIs. The presented RDD–HGSENN technique mainly aims to determine road damages using RSIs. In the presented RDD–HGSENN technique, the RetinaNet model was applied for damage detection on a road. In addition, the RDD–HGSENN technique can perform road damage classification using the ENN model. To tune the ENN parameters automatically, the HGS algorithm was exploited in this work. To examine the enhanced outcomes of the presented RDD–HGSENN technique, a comprehensive set of simulations were conducted. The experimental outcomes demonstrated the improved performance of the RDD–HGSENN technique with respect to recent approaches in relation to several measures.

Intelligent reflecting surfaces (IRS) and power-domain non-orthogonal multiple access (PD-NOMA) have recently gained significant attention for enhancing the performance of next-generation wireless communications networks. More specifically, IRS can smartly reconfigure the incident signal of the source towards the destination node, extending the wireless coverage and improving the channel capacity without consuming additional energy. On the other side, PD-NOMA can enhance the number of devices in the network without using extra spectrum resources. This paper proposes a new optimization framework for IRS-enhanced NOMA communications where multiple drones transmit data to the ground Internet of Things (IoT) devices under successive interference cancellation errors. In particular, the power budget of each drone, PD-NOMA power allocation of IoT devices, and the phase shift matrix of IRS are simultaneously optimized to enhance the total spectral efficiency of the system. Given the system model and optimization setup, the formulated problem is coupled with three variables, making it very complex and non-convex. Thus, this work first transforms and decouples the problem into subproblems and then obtains the efficient solution in two steps. In the first step, the closed-form solutions for the power budget and PD-NOMA power allocation subproblem at each drone are obtained through Karush–Kuhn–Tucker (KKT) conditions. In the second step, the subproblem of efficient phase shift design for each IRS is solved using successive convex approximation and DC programming. Numerical results demonstrate the performance of the proposed optimization scheme in comparison to the benchmark schemes.

The main focus of this manuscript is to study an impulsive fractional integro‐differential equation with delay and Caputo fractional derivative. The existence solution of such a class of fractional differential equations is discussed for linear and nonlinear case with the help of direct integral method. Moreover, Banach's fixed point theorem and Schaefer's fixed point theorem are use to discuss the uniqueness and at least one solution of the said fractional differential equations, respectively. Some hypothesis and inequalities are utilize to present four different types of Hyers–Ulam stability of the mentioned impulsive integro‐differential equation. Example is provide for the illustration of main results. [ABSTRACT FROM AUTHOR]