An iterative method for solving time-fractional partial differential equations with proportional delays

This article deals with an iterative method which is a new formulation of Adomian decomposition method for solving time-fractional partial differential equations (TFPDEs) with proportional delays. The fractional derivative taken here is in Caputo sense. Daftardar-Gejji and Jafari (2006) proposed this new technique where the nonlinearity is defined by using the new formula of Adomian polynomials and the new iterative formula (NIF) is independent of λ. It does not require any discretization, perturbation, or any restrictive parameters. It is shown that the NIF converges rapidly to the exact solutions. Three test problems have been illustrated in order to confirm the efficiency and validity of NIF.Publisher's Versio

A CATEGORICAL CONSTRUCTION OF MINIMAL MODEL

Deleanu, Frei and Hilton have developed the notion of generalized Adams completion in a categorical context; they have also suggested the dual notion, namely, Adams cocompletion of anobject in a category. The concept of rational homotopy theory was first characterized by Quillen. In fact in rational homotopy theory Sullivan introduced the concept of minimal model. In this note under a reasonable assumption, the minimal model of a 1-connected differential graded algebra can be expressed as the Adams cocompletion of the differential graded algebra with respect to a chosen set in the category of 1-connected differential graded algebras (in short d.g.a.’s) over the field of rationales and d.g.a.-homomorphism

On Adams Completion and Cocompletion

The minimal model of a 1-connected differential graded Lie algebra is obtained as the Adams cocompletion of the differential graded Lie algebra with respect to a chosen set of morphisms in the category of 1-connected differential graded Lie algebras (d.g.l.a.’s)over the field of rationals and d.g.l.a.-homomorphisms. The Postnikov-like approximation of a module is obtained as the Adams completions of the space with the help of a suitable set of morphisms in the category of some specific modules and module homomorphisms. The Cartan-Whitehead decomposition of topological G-module is obtained as the Adams cocompletion of the space with respect to suitable sets of morphisms. Postnikov-like approximation is obtained for a topological G-module, in terms of Adams completion with respect to a suitable sets of morphisms, using cohomology theory of topological G-modules.The ring of fractions of the algebra of all bounded linear operators on a separable infinite dimensional Banach space is isomorphic to the Adams completion of the algebra with respect to a carefully chosen set of morphisms in the category of separable infinite dimensional Banach spaces and bounded linear norm preserving operators of norms at most 1. The nth tensor algebra and symmetric algebra are each isomorphic to the Adams completions of the algebras. The exterior algebra and Clifford algebra are each isomorphic to the Adams completions of the algebra with respect to a chosen set of morphisms in the category of modules and module homomorphisms

Effects of Delta-Baryons on Neutron Star Oscillations: Exploring f-Mode Frequencies

In this study, we investigate the effects heavy baryons in neutron stars using the DDMEX model within the Density-Dependent Relativistic Mean Field Theory (DDRMF). We analyze hyperon-free and $\Delta$-admixed hypernuclear matter, revealing insights into composition, emergence, and their effects on properties. The nucleon effective mass is influenced by baryon species, particularly $\Delta$-resonances. Coupling constants impact the equation of state, radius, and maximum mass. Our models align with observations for both scenarios. We explore $\Delta$-resonances role in the dimensionless tidal deformability ($\Lambda$), and their impact on non-radial $f-$mode oscillation frequency.Comment: 17 pages, 10 figure

Thermodynamic Nexus: Investigating the Effect of Temperature and Entropy on the Properties of Neutron Stars with realistic EoS

Neutron Stars (NSs) are often treated as cold, zero-temperature objects in the conventional method of research. However, the recent advances in computational techniques and theoretical modelling have allowed us to probe into the complexities of finite temperature effects and their impact on the behaviour and properties of NSs, unveiling a new frontier in the research field. In this study, we investigate the physical properties, such as mass (M), radius (R), tidal deformability ($\Lambda$), $f$-mode frequency ($f$) etc. of NSs, while considering the effect of temperature (T) and entropy (S) with varying the lepton fractions ($Y_l$). It is observed that those properties are significantly affected by the temperature. First, we study those properties considering a constant temperature throughout the star. However as there is a significant temperature gradient from the star's interior to its surface, it is more appropriate to consider a constant entropy scenario. So we study all the properties using both approaches one with constant temperature and another with constant entropy using BigApple parametrization.Comment: Commets are welcome. This paper is based on master thesis project of Shahebaj Shaik

Dark Matter Admixed Neutron Star in the light of HESS J1731-347 and PSR J0952-0607

This study explores the implications of Dark Matter in Neutron Stars (DMANS) by focusing on two specific astronomical objects: HESS J1731-347 and PSR J0952-0607. Varying the Fermi momentum k$f^{\rm DM}$ of DM, the study analyzes the EOS for the INRS model with and without DM. Results show the robustness of the model, with most EOS curves within chiral Effective Field Theory bounds. Our model predicts a maximum mass of $2.343 \ M_\odot$ for PSR J0952-0607, satisfying NICER bounds. The analysis suggests HESS J1731-347 could be a DMANS. Constraints on DM within NSs are established, and tidal deformability lies within GW event limits. Nonradial $f$-mode oscillations increase with DM, concluding low mass stars pulsate at higher frequencies

The Impact of Anisotropy on Neutron Star Properties: Insights from I-f-C Universal Relations

This study presents a universal relation for anisotropic neutron stars, called the $I-f-C$ relation, which accounts for the local anisotropic pressure using the Quasi-Local (QL) Model proposed by Horvat et al. \cite{QL_Model} to describe the anisotropy inside the neutron star. This study analyzes approximately 60 unified tabulated EoS-ensembles, spanning from relativistic to non-relativistic mean-field models, that comply with multimessenger constraints and cover a broad range of stiffness. The results indicate that the relationship between the parameters becomes more robust with positive anisotropy, while it weakens with negative anisotropy. With the help of the GW170817 \& GW190814 tidal deformability limit, a theoretical limit for the canonical $f$-mode frequency for both isotropic and anisotropic stars is established. For isotropic case the canonical $f$-mode frequency for event GW170817 \& GW190814 is $f_{1.4} = 2.605^{+0.487} _ {-0.459}\ \mathrm{kHz}$ and $f_{1.4} = 2.093^{+0.150} _ {-0.125} \ \mathrm{kHz}$ respectively. These established relationships have the potential to serve as a reliable tool to limit the equation of state of nuclear matter when measurements of relevant observables are obtained.Comment: Comments are welcom

Investigating Dark Matter-Admixed Neutron Stars with NITR Equation of State in Light of PSR J0952-0607

The heaviest pulsar, PSR J0952-0607, with a mass of $M=2.35\pm0.17 \ M_\odot$, has recently been discovered in the disk of the Milky Way Galaxy. In response to this discovery, a new RMF model, "NITR" has been developed. The NITR model's naturalness has been confirmed by assessing its validity for various finite nuclei and nuclear matter (NM) properties, including incompressibility, symmetry energy, and slope parameter values of 225.11, 31.69, and 43.86 MeV, respectively. These values satisfy the empirical/experimental limits currently available. The maximum mass and canonical radius of a neutron star (NS) calculated using the NITR model parameters are 2.35$M_\odot$ and 12.73 km, respectively, which fall within the range of PSR J0952-0607 and the latest NICER limit. This study aims to test the NITR model consistency by applying it to different systems and, consequently, calibrate its validity extensively. Subsequently, the NITR model equation of state (EOS) is employed to obtain the properties of a dark matter admixed neutron star using two approaches: non-gravitational (single fluid) and two-fluid. In the two-fluid model, the dark matter (DM) particles only interact with each other via gravity rather than the nucleons. In both cases, the equation of state becomes softer due to DM interactions, which reduces various macroscopic properties such as maximum mass, radius, tidal deformability, etc. Additionally, through the use of various observational data, efforts are made to constraint the quantity of DM within the NS

Numerical treatment for time fractional order phytoplankton-toxic phytoplankton-zooplankton system

The study of time-fractional problems with derivatives in terms of Caputo is a recent area of study in biological models. In this article, fractional differential equations with phytoplankton-toxic phytoplankton-zooplankton (PTPZ) system were solved using the Laplace transform method (LTM), the Adomain decomposition method (ADM), and the differential transform method (DTM). This study demonstrates the good agreement between the results produced by using the specified computational techniques. The numerical results displayed as graphs demonstrate the accuracy of the computational methods. The approaches that have been established are thus quite relevant and suitable for solving nonlinear fractional models. Meanwhile, the impact of changing the fractional order of a time derivative and time $t$ on populations of phytoplankton, toxic-phytoplankton, and zooplankton has been examined using graphical representations. Furthermore, the stability analysis of the LTM approach has been discussed

OPTIMAL LOT-SIZE DETERMINATION FOR A TWO WARE-HOUSE PROBLEM WITH DETERIORATION AND SHORTAGES USING NPV

Abstract—In this paper, we develop a inventory model for deteriorating items with two warehouses (assuming deterioration rates in the two-warehouses to differ) by minimizing the net present value (NPV) of the total cost. We allow for shortages and complete backlogging and prove here that the optimal replenishment policy not only exists but also is conditionally unique. Further, the result reveals that the reorder interval based on the average total cost, if it exists, must be longer than that derived using NPV. Finally, using a numerical example we illustrate the model and conclude the article with suggestions for possible future research