Emerging as a new field, quantum computation has reinvented the fundamentals of Computer Science and knowledge theory in a manner consistent with quantum physics. The fact that quantum computation has superior features and new events than classical computation provides benefits in proving mathematical theories. With advances in technology, the nonlinear partial differential equations are used in almost every area, and many difficulties have been overcome by the solutions of these equations. In particular, the complex solutions of KdV and Burgers equations have been shown to be used in modeling a simple turbulence flow. In this study, Burger-like equation with complex solutions is defined in Hilbert space and solved with an example. In addition, these solutions were analyzed. Thanks to the Quantum Burgers-Like equation, the nonlinear differential equation is solved by linearizing. The pattern changes of time made the result linear. This means that the Quantum Burgers-Like equation can be used to smoothen the sonic processing.

Blockchain-based data storage methods offer strong data integrity, decentralized security, and transparent access control but also face scalability challenges, high computational costs, and complex data management. This study provides a comprehensive review of on-chain, off-chain, and hybrid storage architectures, analyzing their security vulnerabilities, performance trade-offs, and industry-specific applications. On-chain data storage ensures immutability, data integrity, and high security by storing data directly on the blockchain; however, it is associated with high transaction costs and scalability limitations. In contrast, off-chain solutions reduce costs and enhance performance by storing data outside the blockchain but introduce risks related to data integrity and access security in decentralized environments. Hybrid approaches aim to balance security, cost, and scalability by integrating the strengths of both on-chain and off-chain solutions. This study examines the fundamental components of blockchain-based data storage systems, their sector-specific applications, and the technical challenges they present. Additionally, it explores the trade-offs between security, cost, and decentralization, offering insights into blockchain storage optimization strategies. As a result, this study evaluates the optimization of security protocols, the efficiency of hybrid systems, and the sustainability of distributed storage solutions, contributing to future research in this field.

The IoE forms the foundation of the modern digital ecosystem by enabling seamless connectivity and data exchange among smart devices, sensors, and systems. However, the inherent nature of this structure, characterized by high heterogeneity, distribution, and resource constraints, renders traditional security approaches insufficient in areas such as data privacy, authentication, access control, and scalable protection. Moreover, centralized security systems face increasing fragility due to single points of failure, various AI-based attacks, including adversarial learning, model poisoning, and deepfakes, and the rising threat of quantum computers to encryption protocols. This study systematically examines the individual and integrated solution potentials of technologies such as Blockchain, Edge Computing, Artificial Intelligence, and Quantum-Resilient Cryptography within the scope of IoE security. Comparative analyses are provided based on metrics such as energy consumption, latency, computational load, and security level, while centralized and decentralized models are evaluated through a multi-layered security lens. In addition to the proposed multi-layered architecture, the study also structures solution methods and technology integrations specific to IoE environments. Classifications, architectural proposals, and the balance between performance and security are addressed from both theoretical and practical perspectives. Furthermore, a future vision is presented regarding federated learning-based privacy-preserving AI solutions, post-quantum digital signatures, and lightweight consensus algorithms. In this context, the study reveals existing vulnerabilities through an interdisciplinary approach and proposes a holistic framework for sustainable, scalable, and quantum-compatible IoE security.

The main aim of this manuscript is to obtain numerical solutions for the nonlinear model of interpersonal relationships with time fractional derivative. The variational iteration method is theoretically implemented and numerically conducted only to yield the desired solutions. Numerical simulations of desired solutions are plotted by using Wolfram Mathematica 9. The authors would like to thank the reviewers for their comments that help improve the manuscript.

Randomness plays a crucial role in numerous applications, with cryptography being one of the most significant areas where its importance is evident. A major challenge in cryptographic applications is designing a reliable key generator that meets stringent security requirements. Existing methods often suffer from predictability and fail to provide robust randomness, necessitating novel mathematical approaches. In this study, we propose an innovative mathematical framework that integrates quantum wave functions with chaotic systems to enhance the unpredictability and security of random number generation. The proposed approach leverages the inherent uncertainty of quantum mechanics and the dynamic behavior of chaos to generate statistically strong random sequences. The analysis results confirm that the proposed generator successfully passes all standard statistical randomness tests, demonstrating its effectiveness in cryptographic applications. Additionally, we present a practical implementation of the proposed method as an image encryption algorithm, showcasing its potential for real-world information security solutions. The findings suggest that this approach can contribute significantly to secure communication systems, financial transactions, and other domains requiring high-level cryptographic security.