Mohamed A. Barakat

This paper develops a fractional six-compartment model to describe malware spread in wireless sensor networks. To represent actual network activity, the model is constructed using generalized proportional-Caputo operators that incorporate memory and tempering effects. The existence and uniqueness of solutions are proved by applying fixed-point theorems. The stability of the system is then studied using the Ulam–Hyers approach and its extended form. A fractional Adams predictor–corrector method is employed to illustrate the dynamics. The results suggest that memory and tempering play an important role in shaping infection patterns, and they indicate that fractional calculus can provide a useful framework for studying and managing malware in distributed sensor networks.

In this study we explore the development of a branch of the theory of fractional integration by presenting a new methodological framework based on generalized fractional integrals, focusing on interval functions. This framework enables the more systematic and clear derivation of advanced Hermit-Hadamard inequalities suitable for convex functions. This work integrates Riemann-Liouville fractional inequalities with the classical form of Hermit-Hadamard inequalities for LR convex functions within a unified structure, eliminating the need for separate case studies or independent proofs for each inequality. This research also extends to the development of new Hermite-Hadamard inequalities targeting LR convex functions with interval values, further increasing the comprehensiveness of this proposed framework. The theoretical results obtained in this research are validated through discussions on examples and illustrations that show their application in the field of fractional integration inequalities. Artificial neural networks were also used in this research to correctly forecast the boundaries associated with inequalities in this field, increasing the reliability of this research's results.

Most existing fractional models of COVID-19 describe only the infection process without explicitly accounting for the role of vaccination. In this study, a refined Caputo fractional model is proposed that incorporates a vaccinated class to better understand how immunization influences disease progression. The mathematical formulation guarantees the existence, uniqueness, and positivity of solutions, ensuring that all system trajectories remain biologically valid. The equilibrium points are obtained, and the reproduction number is derived to identify the conditions for disease control. The stability investigation covers local behavior alongside Ulam–Hyers and its extended variants, ensuring the system remains stable under small perturbations. Numerical experiments performed with the Adams–Bashforth–Moulton algorithm illustrate that vaccination reduces infection peaks and shortens the epidemic duration. Overall, the proposed framework enriches fractional epidemiological modeling by providing deeper insight into the combined effects of memory and vaccination in controlling infectious diseases.

One of the best procedures for preventing the spread of the coronavirus is a lockdown, if it is implemented correctly. In order to assess how well lockdowns prevent the virus’s propagation, this paper presents a fractional-order mathematical model constructed by the proportional-Caputo operator. This model consists of five nonlinear fractional-order differential equations. The solution’s existence and uniqueness are investigated using the Schauder and Banach fixed-point theorems. Also, this study produces a stability analysis utilizing Ulam–Hyers and modified Ulam–Hyers criteria. Furthermore, the Adams–Bashforth–Moulton approach is used to implement numerical simulations that show how the model behaves with different parameter combinations and to validate the theoretical results.

In this work, novel Ostrowski-type inequalities for dissimilar function classes and generalized fractional integrals (FITs) are presented. We provide a useful identity for differentiable functions under FITs, which results in special expressions for functions whose derivatives have convex absolute values. A new condition for bounded variation functions is examined, as well as expansions to bounded and Lipschitzian derivatives. Our comprehension is improved by comparison with current findings, and recommendations for future study areas are given.

In this paper, we use a generalized Lipschitzian type condition for a semigroup of self-mappings as employed in Imdad and Soliman (Fixed Point Theory Appl. Vol. (2010), Article ID 692401, 1-14) to prove a fixed point theorem for a generalized Lipschitzian left reversible semitopological semigroup of self-mappings defined on a p-uniformly convex Banach space, besides indicating some possible applications to our main result. Our results generalize and extend some results due to J. S. Jung and B. S. Thakur (Inter. Jour. Math. Math. Sci., 28 (1)(2001), 41-50). 2000 Mathematics Subject Classification. 47H10, 54H25