Mathematical Methods in the Applied Sciences最新文献

Multiterm Dzherbashian-Nersesian (D-N) operators are introduced and an inverse problem for a multiterm fractional integrodifferential equation involving these operators, extending the analysis to the interval $��(�0�,�m�)�$, where $��m�\in �{�\mathbb{Z}�}^{�+�}�$, is investigated. This study reveals new perspectives about existence, uniqueness, and stability of solution within this broader interval. Connecting theoretical advancement with practical applications in physics and engineering, this work not only adds to the theoretical framework but also opens new avenues for real-world applications. Our findings represent a significant shift, offering valuable insights for both theoretical and practical applications in modeling complex systems.

This paper first proves the regularity criteria of the weak solution for the 3D Navier–Stokes equations involving the positive part of the intermediate eigenvalue of the strain matrix in Besov space. And then, it shows two energy conservation criterion of very weak solution via control on integrability of strain tensor. To our best knowledge, for three-dimensional flow, it is the first result of energy conservation criterion by control on the integrability of strain tensor in the $��{�L�}^{�p�}�$ framework.

This paper investigates the dividend problem for a two-dimensional diffusion dual risk model with random delays in profit arrival times. We prove the optimality of threshold dividend strategies. Under this strategy, we derive a set of integro-differential equations for the expected total discounted dividends until ruin. Explicit solutions are obtained when profits follow an exponential distribution, while the Laplace transform method is applied for general profit distributions. Numerical examples validate the theoretical results and analyze parameter effects on the risk model.

This paper proposes a general unifying scheme (GUS) in obtaining the easy-to-check moment stability conditions for nonlinear stochastic differential systems (SDSs). The proposed scheme elucidates a bridge between nonlinear SDSs to positive linear systems (PLSs), which enables the $��p�$-moment stability of nonlinear SDSs can be transformed into 1-moment stability of a related PLS.

The paper deals with the existence and multiplicity of positive solutions for $��(�p�,�q�)�$-Laplacian Kirchhoff-type impulsive fractional differential equations. First, in the degenerate case, we prove that this equation has at least a positive solution based on the mountain pass theorem for any $��\lambda �$ sufficiently large, and the solution converges to zero as $��\lambda �\to �\infty �$. Then, by applying the Ekeland variational principle, at least a positive solution is obtained when $��\lambda �$ is sufficiently small, and the solution converges to zero as $��\lambda �\to �{�0�}^{�+�}�$. Moreover, in the nondegenerate case, we establish the existence of infinitely many solutions by using truncation arguments and Krasnoselskii's genus theory when $��\lambda �$ is sufficiently small.

We explore the well-posedness and regularity of solutions for stochastic Volterra integral equations with general weakly singular kernels (SVIEGK). The kernels considered satisfy $��f�\in �{�L�}^{�1�}�\left(�\right[�0�,�T�\left]�\right)�$ and $��g�\in �{�L�}^{�2�}�\left(�\right[�0�,�T�\left]�\right)�$. By employing a suitably weighted norm and Lebesgue's dominated convergence theorem, we establish the well-posedness of solutions, including their existence, uniqueness, and continuous dependence on the initial value as well as on the parameters $��f�$ and $��g�$. Additionally, for kernels with a specific structure, we extend the Hölder regularity results for stochastic Volterra integral equations.

This work rigorously demonstrates the global-in-time existence of dissipative measure-valued solutions for the Navier–Stokes–Korteweg system describing compressible viscous fluids with intrinsic capillarity effects on periodic spatial domains. Furthermore, we prove a weak–strong uniqueness principle that such dissipative measure-valued solutions coincide with classical solutions when both emanate from identical initial data.

We introduce a concept that generalizes the fractional calculus (differentiation and integration) in the complex domain using the Mellin transform. Special cases that lead to the well-known classical forms are discussed. A real-case example, along with a corresponding plot, is provided for illustration. The fractional derivative mentioned above is utilized to present applications to the differential subordination results of Antonino and Miller, as well as the differential superordination results of Tang et al. for $��p�$-valent analytic functions, ultimately leading to sandwich-type results. Finally, we highlight the potential application of this topic in fluid mechanics.