Mathematical Methods in the Applied Sciences最新文献

This paper deals with the oscillatory behavior of the $��\Psi �$-Hilfer generalized proportional fractional initial value problem. Using the Volterra integral equation and Young's inequality, we establish sufficient conditions for each solution of the problem to oscillate. For the appropriate choice of the kernel $��\Psi �$, our obtained results generalize and recover some existing results in the literature. Additionally, we present some examples to emphasize the importance of our results.

In this paper, we dedicate to investigate complete synchronization of discrete-time fractional-order Cohen–Grossberg neural networks (DFCGNNs) with time delays. In order to resolve the problem, we have made the following efforts. First, we establish a fractional-order convergence principle by employing nabla Laplace transform and analysis techniques. Next, an adaptive nonlinear controller is designed, and then several complete synchronization criteria of DFCGNNs are obtained with the help of inequality techniques and convergence principle we newly establish. Finally, a numerical example is presented to show the validity of theorical results we derive.

In this paper, we consider the following 2D incompressible chemotaxis-Navier–Stokes equations with the fractional diffusion

This study investigates the controllability of a Volterra evolution equation with impulsive terms and nonlocal initial conditions. With the aid of the resolvent operator generated by the linear part of the equation, mild solutions can be defined. Notably, the resolvent operator lacks compactness and equicontinuity. Additionally, the compactness of the impulsive and nonlocal functions is not required. Sufficient conditions for controllability are obtained through measures of noncompactness in Banach spaces. Functional differential equations and hyperbolic partial differential equations can be solved with these results. An example is given to illustrate the validity of the presented results.

This paper deals with a class of fractional neutral delay systems involving proportional Caputo derivative. Maintaining the finite-time stability of fractional-order systems is a major challenge, as their capacity to mimic complex dynamics draws more attention to them. Therefore, the paper presents a novel finite-time stability criterion based on the Banach fixed-point theorem. A decomposition formula for proportional Caputo derivative is provided. This formula allows us to derive a new numerical technique for efficiently solving the proposed problem. Finally, extensive numerical results are performed to illustrate and validate the proposed theoretical results.

In this paper, we investigate the existence, uniqueness, and analysis of two types of $��k�$-Mittag–Leffler–Ulam stabilities in a Volterra integro-differential fractional differential equation that involves the $��(�k�,�\varrho �)�$-Hilfer operator. We utilize the Banach fixed-point theorem to establish the existence and uniqueness of solutions. We examine the stability properties, including the $��k�$-Mittag–Leffler–Ulam–Hyers $��k�$-$��M�L�U�H�$ and k-Mittag–Leffler–Ulam–Hyers–Rassias $��k�$-$��M�L�U�H�R�$ stabilities, by employing the Grönwall–Bellman inequality. Additionally, we provide an example to confirm our findings.

In this paper, the full compressible Navier-Stokes equations with Cattaneo's heat transfer law or revised Maxwell's law are considered. We present a loss of initial smoothness of smooth solutions within a finite time and give an upper bound of such time. It is not required that the initial data has compact support or contains vacuum in any finite regions. Moreover, the blow-up result has no restriction about the specific heat ratio. The main approach is motivated by previous studies and constructing a differential inequality.

By using variational methods, we study a class of discrete nonlinear Schrödinger systems, where the potentials are bounded and the nonlinearities are composed of perturbed and concave–convex terms. The main novelties of this paper are as follows: (1) some perturbed terms and concave–convex terms are added to the systems, (2) the weight functions can be sign-changing, and (3) the potentials are bounded, which is essentially different from the unbounded potentials studied before.

The free metaplectic transform (FMT), a generalized form of the linear canonical transform (LCT), has proven to be a useful analytical tool in signal processing applications. This paper aims to generalize the FMT to a quaternionic framework involving the two-dimensional signals. We further study some properties that correspond to those of the standard ones, including linearity, uniform continuity, inversion, and Parseval's identity for this new integral transform, which we coin as the quaternionic free metaplectic transform (QFMT). Furthermore, utilizing the relationship between the general quaternionic Fourier transform and the QFMT, several uncertainty principles (UPs) for the QFMT are established, including the Heisenberg–Weyl UP, Hardy UP, logarithmic UP, Donoho–Stark UP, and entropic UP. We expect that this paper will open up avenues of promising research and applications involving this new transformation.

In this paper, we consider the spatiotemporal dynamics behaviors of a Leslie–Gower diffusion predator–prey system with prey refuge and Beddington–DeAnglis (B-D) functional response. By using the Poincaré inequality and topological degree theory, we first investigate the Turing instability of the reaction–diffusion system and prove the existence of nonconstant positive steady-state solutions. Then we discuss the steady-state bifurcation and the direction to Hopf bifurcation of the PDE model by the local bifurcation theorem and center manifold theory. Finally, some numerical simulations are presented to supplement the analytic results in one dimension which indicates that changes in prey refuge and diffusion coefficient can increase the complexity of the system.