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Nowadays, the construction of a fractional-order hyperchaotic memristive system (FOHMS) and its real-world applications are fascinating and have received keen attention. A new 5D fractional-order hyperchaotic memristive system that uses a flux-controlled memristor with quadratic nonlinearity is introduced in this paper. The multiple line equilibrium, chaos, hyperchaos, coexisting attractors, periods and limit cycles are the fascinating aspects of this hyperchaotic system. The complex characteristic dynamics such as symmetricity, dissipativity, Lyapunov dynamics, equilibrium point stability and bifurcation diagram of the proposed hyperchaotic system are illustrated in both theoretical and graphical manners. For a particular set of parameter values, curious metastability, which shows transient transfer behaviour, has been discovered. Moreover, complete dislocated general hybrid projective synchronization and a new enhanced digital image algorithm have been introduced based on the 5D FOHMS. The effectiveness of the proposed algorithm has been visualized for various fractional derivatives, which shows the importance of the presented scheme in the digital world.

This paper constructs and analyzes the dynamical properties of a new fractional-order real hyper-chaotic system and its corresponding complex variable system. A thorough analysis was done by employing stability of equilibrium points, phase plots, Lyapunov spectrum, and bifurcation analysis for the consequences of varying fractional-order derivative and parameter values on the system. For the first time, a modulus synchronization scheme is proposed to synchronize real and complex fractional-order dynamical systems. Based on Lyapunov stability theory, non-linear controllers are designed to achieve the proposed modulus synchronization scheme. A new modulus synchronization encryption algorithm with a large key space size for digital images is introduced for the application. The experimental results and analysis validate the desired algorithm. Also, we compare our result of the new encryption algorithm with the previously published literature and verify the efficacy of the considered scheme. Numerical simulations are given to validate the theoretical analysis

In this paper, the stability conditions and chaotic behaviors of new different fractional orders of reverse butterfly-shaped dynamical system are analytically and numerically investigated. Designing an appropriate feedback controller, the fractional order chaotic system is synchronized. Applying the synchronized fractional order systems in digital cryptography, a well secured key system is obtained. The numerical simulations are given to validate the correctness of the proposed synchronized fractional order chaotic systems and proposed key system.

Given a holomorphic self-map $\\varphi $ of $\\mathbb {D}$ (the open unit disc in $\\mathbb {C}$ ), the composition operator $C_{\\varphi } f = f \\circ \\varphi $ , $f \\in H^2(\\mathbb {\\mathbb {D}})$ , defines a bounded linear operator on the Hardy space $H^2(\\mathbb {\\mathbb {D}})$ . The model spaces are the backward shift-invariant closed subspaces of $H^2(\\mathbb {\\mathbb {D}})$ , which are canonically associated with inner functions. In this paper, we study model spaces that are invariant under composition operators. Emphasis is put on finite-dimensional model spaces, affine transformations, and linear fractional transformations.

Thermal fluctuations, which occur in extreme climatic condition, increase the energy consumption of building. To solve the above issue, thermal insulation materials, which are used commonly in the current practice possess several practical limitations and issues such as reduction of net floor area, increase in dead weight of building, susceptibility to deterioration, and variation in thermal conductivity with changes in humidity and temperature. Hence, to address the above issues, this study mainly focuses to use low thermal conductive and high heat storage phase change material (PCM) in building. In order to get the maximum surface area of PCM, it is incorporated in cement mortar for non-structural applications in building. The micro-encapsulated phase change material (MPCM) used in the study has phase change temperature of 28°C, and latent energy of 183 kJ/kg. It is incorporated in mortar to replace some of the fine aggregate (5 and 10% by weight) to find its effects on mechanical and thermal properties. From the test results on mechanical behaviour, it is observed that incorporation of 10% MPCM by weight of fine aggregate reduced compressive strength by 70% and flexural strength by 61%. However, the achieved strength of MPCM incorporated mortar is sufficient for non-structural applications. Also, it was observed that 10% MPCM added to mortar decreased its thermal conductivity by 22%, increasing the material's thermal insulation. In addition, 10% MPCM incorporated mortar having 1 m 2 surface area and 10 mm thick can store 246 kJ heat energy, which will further improve thermal comfort in building. Further, from thermal stability analysis of MPCM, it is observed that MPCM has no effect on thermal stability of mortar up to 250°C. Adding to above, the results of economic analysis are also found to be promising as the payback period of incorporated MPCM varies approximately from 4.54 to 7.56 years based on 100% to 60% utilization period in a year.

Submarine groundwater discharge (SGD) acts as a carrier for elements, nutrients and pollutants into the ocean. This study estimated SGD along the Kanyakumari coast of India, using the Radon and nutrient mass balance approach. Groundwater and porewater samples during the high-tide and low-tide conditions showed Radon ( 222 Rn) concentrations between 11.68 and 66.96 Bq/L during the pre-monsoon and between 18.9 and 189.56 Bq/L during the post-monsoon, with an inverse relationship with EC (256–52400 µS/cm: pre-monsoon and 329–48000 µS/cm: post-monsoon). SGD, estimated using the radon mass balance approach, ranged from 0.01 to 0.54 m 3 m −2 d −1 in pre-monsoon and 0.04 to 0.98 m 3 m −2 d −1 in post-monsoon. Mean nutrient concentrations for DIN, DIP, and DSi in both seasons were 0.79-2.0, 0.21–0.28, and 17.22–20.75 µmol L − 1 , respectively. In a strategic part of Indian coast, this study enabled the location and determination of SGD and thereby provided valuable data for adopting proper methodology to mitigate the issue of groundwater scarcity and pollution.

This paper aims to investigate stochastic fractional Schrödinger evolution equations with potential and Poisson jumps in Hilbert space. The solvability of the proposed system is established by using fractional calculus, semigroup theory, Krasnoselskii’s fixed point theorems and stochastic analysis. Furthermore, sufficient conditions are formulated and proved to assure that the mild solution decays exponentially to zero in the square mean. Lastly, an application is given to demonstrate the developed theory.

In this study, a novel 5-D hyperchaotic system is constructed by employing the circular restricted three body problem (CRTBP). The existence of hyperchaos is confirmed by Lyapunov exponents and shows that they have a symmetrical structure. The system exhibits a five-petal flower shaped hyperchaotic attractor. The synchronization and control of two identical hyperchaotic systems are accomplished via a tracking control system. The simulation results showed the effectiveness of the tracking and synchronization control systems. An innovative property of the proposed system has been identified and shows its ability to generate an infinitely many different-shaped chaotic attractors with finite wings by varying only the systems parameters.

In this paper, the problem of finite-time stability for a class of fractional-order Cohen–Grossberg BAM neural networks with time delays is investigated. Using some inequality techniques, differential mean value theorem and contraction mapping principle, sufficient conditions are presented to ensure the finite-time stability of such fractional-order neural models. Finally, a numerical example and simulations are provided to demonstrate the effectiveness of the derived theoretical results.

In this study, a fractional order dynamical system in four dimensions is constructed. It is found that the proposed system displays multi-scroll chaotic attractors without modifying the nonlinear functions and parameter values inside the system. Furthermore, the multi-scale synchronization between two identical multi-scroll fractional chaotic systems is achieved by applying sliding mode control theory. Inspired by the applications of fractional order dynamical systems, synchronized fractional multi-scroll chaotic systems are used to built a new key agreement protocol for all kinds of cryptosystems. The efficiency and security of the key agreement protocol are examined. Using numerical examples, the anticipated theoretical results are demonstrated.