Dnyaneshwar Dadaji Pawar

We investigate the cosmological implications of a non‐minimally coupled gravity model within the symmetric teleparallel framework, in which the non‐metricity scalar is coupled to the matter Lagrangian , where both curvature and torsion vanish identically. This framework is a specific form of the gravitational action that includes a coupling term , thereby extending ‐gravity. We consider a power‐law parameterization of the coupling functions and evaluate the Hubble parameter . We use observational hubble data (OHD), the Union3 supernova compilation, dark energy spectroscopic instrument data release 2 (DESI DR2) baryon acoustic oscillation (BAO) data, and their joint datasets to constrain the model parameters with the Markov Chain Monte Carlo (MCMC) technique. The obtained model transitions from a decelerating state to an accelerating state and exhibits the quintessence model in late times. Furthermore, we discuss the various physical features of the model to show the model's physical viability. Additionally, we examine the Misner–Sharp mass as a bridge between geometry and thermodynamics, providing a quasi‐local measure of energy in spherically symmetric space‐times and linking spacetime dynamics to thermodynamic laws in modified gravity.

In this paper, we study late time cosmology in the teleparallel framework using a simple and data driven form of the Hubble rate, [Formula: see text]. We test nonlinear model [Formula: see text]. This setup keeps the background fully analytic and gives closed expressions for [Formula: see text], [Formula: see text], and [Formula: see text]. We fit the model to 57 observational Hubble measurements and to the Pantheon supernova sample and obtain tight best fit values for [Formula: see text] and [Formula: see text]. The model follows the observed rise of [Formula: see text] up to [Formula: see text] and matches the distance modulus over the full range. The deceleration parameter shows the expected change of sign. The transition redshift is [Formula: see text] for the Hubble data and [Formula: see text] for the Pantheon data. Today we find [Formula: see text], which confirms ongoing acceleration. The Om diagnostic is nearly constant near [Formula: see text] and close to the [Formula: see text]CDM value. It changes only mildly at higher redshift and shows no unphysical features. The pressure is negative at late times and the energy condition combinations behave in a regular way. This is consistent with an accelerating effective fluid. Information criteria such as AIC and BIC prefer [Formula: see text]CDM for the same Hubble set, but our teleparallel models still track the data well and allow controlled departures at earlier epochs. Overall, this framework gives a compact and clear description of cosmic acceleration that agrees with present data.

This paper presents a spectral collocation method based on shifted Chebyshev polynomials of the third kind (SCP3) for the numerical solution of variable‐order fractional differential equations (VO‐FDEs). The SCP3 basis is employed to construct accurate approximations of the unknown solution over the interval [0, 1], exploiting its orthogonality and favorable approximation properties. An operational matrix formulation is developed to represent both integer‐order derivatives and VO Caputo fractional derivatives in a unified algebraic framework. This formulation transforms the original VO‐FDEs into a system of algebraic equations, enabling efficient numerical implementation. A theoretical analysis is provided, including error representation and convergence analysis. The proposed method exhibits algebraic convergence for sufficiently smooth solutions and spectral convergence for analytic functions. The applicability and performance of the method are demonstrated through several numerical examples, including linear, nonlinear, and coupled variable‐order fractional systems.

This paper presents a novel and efficient spectral collocation framework for solving nonlinear variable‐order fractional differential equations (VO‐FDEs) involving the Atangana–Baleanu–Caputo (ABC) operator. Shifted Morgan‐Voyce polynomials (SMVPs) are employed as basic functions to construct a new operational matrix specifically adapted to the variable‐order ABC operator. This matrix substantially reduces computational complexity while maintaining high accuracy. The proposed approach converts VO‐FDEs into tractable nonlinear algebraic systems. In contrast to existing polynomial‐based techniques, the framework demonstrates enhanced robustness in handling nonlinearities and variable memory effects, delivering superior precision and stability. Numerical experiments are conducted on challenging nonlinear and multiterm VO‐FDEs. Comparative analyses confirm the advantages of the Morgan–Voyce polynomials (MVPs)‐based scheme over classical spectral methods. These findings establish the proposed method as a versatile and reliable tool for tackling complex VO‐FDEs with nonsingular memory kernels.

In this article, we explore the application of the double ARA-Kamal transformation (DARA-KT) to the nonlocal fractional Caputo derivative operator. Our investigation yields intriguing findings, particularly in solving certain classes of fractional partial differential equations (FPDEs). We delve into various physical scenarios, including Wave, Klein-Gordon, and Fokker-Planck equations, analyzing their implications. The incorporation of the DARA-KT technique proves to be both efficient and precise in deriving exact solutions for FPDEs. To demonstrate the practicality of our approach, we present some numerical examples and figures.

In this study, we investigate anisotropic Bianchi Type VI cosmological model within the framework of fractal universe. By utilizing the energy–momentum tensor for a perfect fluid, we solve the corresponding field equations. In this study, we derive leading cosmological parameters, including the hubble parameter H and deceleration parameter q in terms of cosmic time and redshift also. To determine the model parameters such as k, [ ] and the hubble constant [ ], the hubble dataset was analyzed using the [ ] test. This analysis reveals the best-fit values of [ ], [ ], [ ], [ ] and [ ] match with the [ ]CDM model. We carry blow-by-blow analysis of the model’s characteristics via energy density [ ], pressure p and EoS parameter. We examine whether the energy conditions — null energy condition (NEC), strong energy condition (SEC), weak energy condition (WEC) and dominant energy condition (DEC) — are satisfied. Furthermore, the diagnostic parameters are analyzed to evaluate the deviation of the obtained model from the [ ]CDM model and to classify various dark energy models during the universe’s expansion. The om diagnostic is depicted as a function of redshift for [ ] and [ ] revealing that [ ] settles around [ ] with slight deviation in the range [ ]. The model closely aligns with [ ]CDM at higher redshifts. The pair of statefinder diagnostics r versus s is also discussed, and our model for [ ] represents the [ ]CDM model.