Mathematical Methods in the Applied Sciences最新文献

In this paper, we establish the global stability and large time behavior of strong solutions to the compressible Oldroyd-B model without stress diffusion in $��{�𝕋�}^{�3�}�$. In addition, the $��{�H�}^{�3�}�$-norm of the solutions is shown to be stable and decay exponentially in time by a bootstrap argument. In particular, we extend Liu-Lu-Wen's result (SIAM J. Math. Anal., 53 (2021), 6216–6242) to the bounded domains, where they consider the Cauchy problem and obtain the algebraic decay behavior of strong solution.

This paper establishes the existence and uniqueness (EU) of solutions for a class of pantograph fractional integro-stochastic differential equations (PFISDEs) via the Banach fixed point theorem (BFPT). Furthermore, the Ulam–Hyers stability (UHS) is analyzed using Gronwall's inequality. The applicability of the theoretical findings is demonstrated through two illustrative examples.

The COVID-19 pandemic has highlighted the critical importance of effective vaccination strategies in controlling the spread of the virus. With the emergence of new variants and waning immunity, booster vaccinations have gained attention as a potential tool to enhance individual and population-level protection. Using the principles of optimal control theory, this study aims to ascertain the impact of boosters on the patterns of COVID-19 propagation. By formulating an appropriate mathematical model, we will design optimal control strategies to evaluate the impact of booster doses on key epidemiological parameters. Further, the conditions for disease-free equilibrium, stability, and reproduction number for the addressed model are calculated. In particular, global stability is examined using the Lyapunov function. The corresponding crucial optimality requirements were also derived. To represent the memory effect in epidemics, the proposed model is driven using fractional differential equations. The existence and uniqueness and boundedness of fractional model are derived. We undertake numerical simulations by taking real-time data in India for reflecting the impact of booster vaccination efficacy. Finally, graphical interpretation is shown and explored in depth. Our results reveal that to control the COVID-19 pandemic, booster vaccination is effective and efficient in addition to vaccination and quarantine.

In the constitutive equation of the heat flux with kernel in the form of a general fractional derivative of Riesz type, the time delay of the form $��t�-�\frac{�\left(�x�-�\xi �\right)�}{�c�}�$ is introduced. The resulting generalized heat conduction equation is derived. The influence of parameters on the solution is studied numerically.

This article examines the unique solvability of a boundary value problem for hyperbolic systems under periodic conditions. To solve the stated problem, the Dzhumabaev method is employed, which transforms the original boundary value problem into an equivalent multipoint boundary value problem for ordinary differential equations with parameters, incorporating both initial and additional boundary conditions. Furthermore, the study establishes a connection between the unique solvability of the original problem and the invertibility of the matrix $��Q�$. Recurrent relations for determining the elements of the inverse matrix are also derived.

In this article, we introduce a new class of $��{�\Delta �}_{�h�}�$ truncated exponential-based Appell polynomials and investigate their key properties and identities. The study further explores their connection with the monomiality principle, providing a deeper algebraic structure. Extensions of this framework lead to the construction of $��{�\Delta �}_{�h�}�$ truncated exponential-based Bernoulli, Euler, and Genocchi polynomials, along with their respective properties. Further, the generating relation and operational identity for these polynomials are established using fractional operators. Numerical evaluations of these special cases are presented, and the distribution of their zeros is visualized using Mathematica. The paper concludes with a summary of results and suggestions for future research directions.

This paper introduces a novel numerical methodology employing wavelet-based $��L�2�$-$��{�1�}_{�\sigma �}�$ discretization and its higher order convergence analysis to address the time-fractional Black-Scholes model within a jump-diffusion framework, specifically in the context of pricing European options. The Haar wavelet approximation is applied to solve the resulting semi-discrete problem, and the fractional time operator is effectively approximated through $��L�2�$-$��{�1�}_{�\sigma �}�$ discretization. The theoretical estimates of the error bounds are provided. A detailed analysis demonstrates that the method yields a second-order accuracy over the space-time domain, depending on the solution's regularity as required for theoretical convergence. Moreover, the study explores the impact of fractional operators on option pricing through various test examples and applications based on Merton's as well as Kou's jump-diffusion model. We rigorously compared our results with the spline-based finite difference method and an implicit finite difference method, explicitly highlighting the efficacy and accuracy of our proposed method. In addition, the present research contributes not only to a robust numerical solution for time-fractional Black-Scholes models but also valuable insights into the influence of fractional operators on option pricing dynamics under jump-diffusion.