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In this paper, we construct an isotropic cosmological model in the $ f(Q, T) $ theory of gravity in the frame of a flat FLRW spacetime being $ Q $ the non-metricity tensor and $ T $ the trace of the energy-momentum tensor. The gravity function is taken to be a quadratic equation, $ f(Q, T)=\zeta Q^2 + \gamma T $, where $ \zeta<0 $ and $ \gamma $ are the arbitrary constants. We constrain the model parameters $ \alpha $ and $ H_0 $ using the recent observational datasets: the Hubble dataset (OHD), the Pantheon dataset of $ 1048 $ points, and the joint dataset (OHD + Pantheon). The universe model transits from an early deceleration state to an acceleration in late times. This model also provides the ekpyrotic phase of the universe on the high redshift $ z>12.32 $. In this model, the Big Bang is described as a collision of branes, and thus, the Big Bang is not the beginning of time. Before the Big Bang, there is an ekpyrotic phase with the equation of state $ \omega >> 1 $. In late times, the undeviating Hubble measurements reduce the $ H_0 $ tension in the reconstructed $ f(Q, T) $ function. Additionally, we study various physical parameters of the model. Finally, our model describes a quintessence dark energy model at later times., Comment: 17 pages, 18 figures

We investigate the universe's evolution within the framework of Rastall gravity, which is an extension of the standard $\Lambda$CDM model. Utilizing a linear parametrization of the Equation of State (EoS) in a Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) background, we constrain the model parameters through analysis of cosmic chronometers (CC), Pantheon, Gold, Gamma Ray Burst (GRB), and Baryon Acoustic Oscillations (BAO) datasets, as well as their joint analysis, under $1\sigma$ and $2\sigma$ confidence levels, considering the Rastall parameter $\lambda$. The constrained parameters are then used to compare our model with the standard $\Lambda$CDM model. Our findings include a detailed examination of the model's physical interpretations and demonstrate the potential for an accelerating universe expansion in later times, aligning with the observed behavior of dark energy., Comment: 21 pages, 19 figures, accepted for publication in Physica Scripta

In this investigation, we perform an observational statistical analysis in the theory of $ f(R, L_m) $ gravity. The proposed theoretical model is based on the Ricci scalar's non-linear contribution. We use a distinct parameterization for the deceleration parameter and constrain the model parameters by using various observational data. To determine the best-fit model for the cosmological parameters, we use different observational datasets such as the Hubble Space Telescope, the Pantheon Supernova Survey, the Gold dataset, the Gamma-Ray Burst (GRB), and the Baryon Acoustic Oscillations (BAO). Furthermore, we study the late-time cosmic evolution of the Universe in detail and examine the implications of the constraint values on cosmological parameters. Additionally, we conduct a thorough comparison with the standard cosmological model $ \Lambda $CDM and other standard models obtained by Odintsov et al. \cite{Odintsov:2023cli, Odintsov:2024lid} to examine the validity of our proposed model in the low-redshift regimes. Finally, we find that the proposed model encapsulates an intriguing transition from early deceleration at high redshift to acceleration at low redshift, a quintessence dark energy scenario, and convergence towards the well-established $ \Lambda $CDM model in late-time Universe's evolution., Comment: 18 pages, 15 figures

We study a cosmological model in Rastall's theory of gravity in the framework of the flat FLRW metric. We formulate the value of the Hubble parameter, which contains two model parameters, $ \alpha $ and $ j $. Employing the Markov Chain Monte Carlo (MCMC) sampling technique, we determine the values of these model parameters along with their uncertainties. Moreover, we derive the equation of state (EoS) parameter, which converges around the quintessence region. We perform a dynamical system analysis using the linearization technique to validate the results independently. Also, we discuss various physical attributes of the model, highlighting the transition to acceleration and the violation of the strong energy condition (SEC) in the late stages of evolution. In conclusion, our model mimics the behavior of a dark matter fluid during the past epoch and transitions into a quintessence dark energy model in the future epoch., Comment: 18 pages, 17 figures

We propose a novel cosmological framework within the $f(R,T)$ type modified gravity theory, incorporating a non-minimally coupled with the higher order of the Ricci scalar ($R$) as well as the trace of the energy-momentum tensor ($T$). Therefore, our well-motivated chosen $f(R,T)$ expression is $ R + R^m + 2 \lambda T^n$, where $\lambda$, $m$, and $n$ are arbitrary constants. Taking a constant jerk parameter ($j$), we derive expressions for the deceleration parameter ($q$) and the Hubble parameter ($H$) as functions of the redshift $z$. We constrained our model with the recent Observational Hubble Dataset (OHD), $Pantheon$, and $ Pantheon $ + OHD datasets by using the analysis of Markov Chain Monte Carlo (MCMC). Our model shows early deceleration followed by late-time acceleration, with the transition occurring in the redshift range $1.10 \leq z_{tr} \leq 1.15$. Our findings suggest that this higher-order model of $f(R,T)$ gravity theory can efficiently provide a dark energy model for addressing the current scenario of cosmic acceleration., Comment: 14 pages, 12 figures

This paper presents an efficient numerical technique for solving multi-dimensional fractional optimal control problems using fractional-order generalized Bernoulli wavelets. The numerical results obtained by this method have been compared with the results obtained by the method using orthonormal Bernoulli wavelets. Using fractional-order generalized Bernoulli wavelets, product and integral operational matrices have been obtained. By using these operational matrices, the multi-dimensional fractional optimal control problems have been reduced into a system of algebraic equations. To confirm the efficiency of the proposed numerical technique involving fractional-order generalized Bernoulli wavelets, numerical problems have been solved by using both orthonormal Bernoulli wavelets and fractional-order generalized Bernoulli wavelets and obtaining an approximate cost function value, which has been found by approximating state and control functions. In addition, the convergence rate and error bound of the proposed numerical method have also been derived., Comment: arXiv admin note: substantial text overlap with arXiv:2310.06570

This paper presents an efficient numerical method for solving fractional optimal control problems using an operational matrix for a fractional wavelet. Using well-known formulae such as Caputo and Riemann-Liouville operators to determine fractional derivatives and integral fractional wavelets, operational matrices were devised and utilised to solve fractional optimal control problems. The proposed method reduced the fractional optimal control problems into a system of algebraic equations. To validate the effectiveness of the presented numerical approach, some illustrative problems were solved using fractional Taylor and Taylor wavelets, and the approximate cost function value derived by approximating state and control functions was compared. In addition, convergence rate and error bound of the proposed method have been derived.