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This paper presents a reduced-order Legendre–Galerkin extrapolation (ROLGE) method combined with the scalar auxiliary variable (SAV) approach (ROLGE-SAV) to numerically solve the time-fractional Allen–Cahn equation (tFAC). First, the nonl...

Modern power distribution networks are increasingly challenged with nonlinear operating conditions, the high penetration of distributed energy resources, and conflicting operational objectives such as loss minimization and voltage regulation. Existin...

This study addresses the issue of nonfragile state estimation for fractional-order memristive neural networks with time-varying delays under an adaptive event-triggered mechanism. Possible gain perturbations of the estimator are considered. A Bernoul...

This paper introduces the concepts of inward-β-enriched Reich multi-valued contractions and outward-β-enriched Reich multi-valued contractions in the context of normed linear spaces. We establish fixed point existence theorems for these gen...

For the first time, this paper introduces Nabla fractional calculus into the distributed Nash equilibrium (NE) seeking problem of aggregative games (AGs) with partial decision information in undirected communication networks, and proposes two novel f...

This paper aims to address the data-driven feedback control problem of Delta fractional-order systems. First, we convert the studied system into an integer-order discrete-time system with progressively increasing time delays. A novel stability condit...

This paper presents a novel high-order numerical method. The proposed scheme utilizes polynomial generating functions to achieve p order accuracy in time for the Grünwald–Letnikov fractional derivatives, while maintaining second-order spat...

The aim of the current manuscript is to study a coupled system of nabla fractional equations with general summation boundary conditions depending on parameters. We deduce the expression of the Green’s function and we obtain useful bounds of it....

Unique fractal characteristics are significantly controlled by shale lithofacies, mineralogical characteristics, and OM features, which in turn determine reservoir properties and gas-bearing capacity. However, a comprehensive understanding of fractal...

The graph Hilbert transform (GHT) is a key tool in constructing analytic signals and extracting envelope and phase information in graph signal processing. However, its utility is limited by confinement to the graph Fourier domain, a fixed phase shift...