Abdel-Haleem Abdel-Aty

In this study, we explore a new exact solution for a charged spherical model as well as the astrophysical implications of the torsion parameter χ1 and electric charge Q on compact stars in lower mass gaps in the $f(\mathcal {T})$ gravity framework. Commencing with the field equations that describe anisotropic matter distributions, we select a well-behaved ansatz for the radial component of the metric function, along with an appropriate formulation for the electric field. The resulting model undergoes rigorous testing to ensure its qualification as a physically viable compact object within the $f(\mathcal {T})$ gravity background. We extensively investigate two factors: χ1 and Q, carefully analyzing their impacts on the mass, radius, and stability of the star. Our analyses demonstrate that our models exhibit well-behaved behavior, free from singularities, and can successfully explain the existence of a wide range of observed compact objects. These objects have masses ranging from $0.85^{+0.15}_{-0.15}$ to 2.67 M⊙, with the upper value falling within the mass gap regime observed in gravitational events like GW190814. A notable finding of this study has two aspects: we observe significant effects on the maximum mass (Mmax) and the corresponding radii of these objects. Increasing values of χ1 lead to higher Mmax (approximately $2.64^{+0.13}_{-0.14}$) and smaller radii (approximately $10.40^{+0.16}_{-0.60}$), suggesting the possibility of the existence of massive neutron stars within the system. Conversely, increasing values of Q result in a decrease in Mmax (approximately $1.70^{+0.05}_{-0.03}$) and larger radii (approximately $13.71^{+0.19}_{-0.20}$). Furthermore, an intriguing observation arises from comparing the results: for all values of χ1, nonrotating stars possess higher masses compared to slow-rotating stars, whereas this trend is reversed when adjusting Q.

In this manuscript, a new form of the generalized q-deformed Sinh-Gordon equation is investigated which could model physical systems with broken symmetries and to incorporate phenomena involving amplification or dissipation. The proposed model is explored based on the Lie symmetry approach. Using similarity reduction, the partial differential equation is transformed into an ordinary differential equation. By employing the generalized auxiliary equation approach, precise results for the derived equation are obtained. The solutions are graphically depicted as 3D, 2D, and contour plots. Furthermore, the qualitative analysis of the considered model is investigated by employing the concepts of bifurcation and chaos. The phase profiles are displayed for different sets of the parameters. Additionally, by applying an external periodic strength, quasi-periodic and chaotic behaviors are documented. Various tools for detecting chaos are discussed, including 3D and 2D phase patterns, time series, and Poincaré maps. Additionally, a sensitivity analysis is conducted for various initial conditions. The obtained findings are unique and indicate the viability and efficacy of the suggested strategies for evaluating soliton solutions and phase illustrations for various nonlinear models.

In this paper, we investigate new types of nonlocal implicit problems involving piecewise Caputo fractional operators. The existence and uniqueness results are proved by using some fixed point theorems. Furthermore, we present analogous results involving piecewise Caputo-Fabrizio and Atangana–Baleanu fractional operators. The ensuring of the existence of solutions is shown by Ulam-Hyer’s stability. At last, two examples are given to show and approve our outcomes.