Mohammad Bagher Ghaemi

In this paper, we study a coupled system of fractional Volterra integral equations in the ∗‐fuzzy measure spaces that are equipped with an Archimedean triangular norm and a ∗‐fuzzy integral. Setting a Lipschitz condition on the nonlinear kernels, defining a suitable ∗‐fuzzy control function, and applying the alternative fixed‐point method, we obtain existence, uniqueness, and Hyers–Ulam stability of this system in an admissible ∗‐fuzzy function space. We also analyze the Lipschitz‐type dependence of the solution on the fractional orders over compact intervals. Finally, we consider the Hamacher ∗‐fuzzy product‐integration Picard scheme and solve the equation numerically. Our results extend and enhance the previous studies in the literature.

This paper presents a new framework of pseudo‐–fractional calculus in generalized Banach spaces by bringing together pseudo‐analysis, –calculus, and quantum calculus. We introduce Liouville–Caputo and Riemann–Liouville pseudo‐–fractional operators and outline their main properties. Then, by applying the Banach fixed point principle, we establish the existence and uniqueness of solutions for a pseudo‐–fractional differential system, extending classical fractional and –fractional theories.

In this article, we successfully generalize the SEIR (Susceptible, Exposed, Infected, and Recovered) model to account for random and intermittent instances of disease transmission. This model explains the increased probability of disease transmission during specific periods, particularly for seasonal illnesses. Furthermore, we investigate the conditions necessary to ensure at least one solution for this model by employing the measure of noncompactness. Following this, we introduce a new approach that examines convergence, after which we apply the proposed numerical method to study practical examples.

This study explores the existence and Mittag–Leffler stability of solutions for fuzzy fractional systems that include Caputo derivatives and ordinary derivatives with non-local conditions using the Schauder fixed-point theorem. Following this, we employ the Laplace transform method and numerical techniques to create iterative methods for obtaining exact and approximate solutions.

This paper examines the stability of a fractional‐order model that describes the free‐fall motion of a football in changing environmental conditions. Traditional models often overlook memory effects and nonlocal influences like air resistance, humidity, and turbulence. To tackle this issue, we enhance the classical Newtonian model by using the Hilfer fractional derivative, which includes memory and hereditary properties. We analyze the resulting equation for Ulam–Hyers–Rassias stability within the context of random Banach spaces, using distribution‐valued norms and t –norms to manage uncertainty and oscillatory behavior. We apply fixed‐point theory to establish sufficient conditions for stability and uniqueness of solutions. Numerical simulations and error analyses with special functions show the effectiveness and reliability of the proposed model, demonstrating better accuracy and stability compared to traditional methods.