Exact Solutions and Finite Time Stability of Linear Conformable Fractional Systems with Pure Delay

We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay.By using new conformable delayed matrix functions and the method of variation,we obtain a representation of their solutions.As an application,we derive a finite time stability result using the representation of solutions and a norm estimation of the conformable delayedmatrix functions.The obtained results are new,and they extend and improve some existing ones.Finally,an example is presented to illustrate the validity of our theoretical results.

Comprehensive analysis of relativistic embedded class-I exponential compact spheres in f(R,φ)gravity via Karmarkar condition

In this article,we use the prominent Karmarkar condition to investigate some novel features of astronomical objects in the f(R,φ)gravity;R andφrepresent the Ricci curvature and the scalar field,respectively.It is worth noting that we classify the exclusive set of modified field equations using the exponential type model of the f(R,φ)theory of gravity f(R,φ)=φ(R+α(eβR-1)).We show the embedded class-I approach via a static,spherically symmetric spacetime with an anisotropic distribution.To accomplish our objective,we use a particular interpretation of metric potential(grr)that has already been given in the literature and then presume the Karmarkar condition to derive the second metric potential.We employ distinct compact stars to determine the values of unknown parameters emerging in metric potentials.To ensure the viability and consistency of our exponential model,we execute distinct physical evolutions,i.e.the graphical structure of energy density and pressure evolution,mass function,adiabatic index,stability,equilibrium,and energy conditions.Our investigation reveals that the observed anisotropic findings are physically appropriate and have the highest level of precision.

Traversable wormhole solutions in the f(R)theories of gravity under the Karmarkar condition

This paper examines traversable wormhole models in the f(R) theories of gravity by applying the Karmarkar condition. For this purpose, we consider spherically symmetric space-time to examine the structure of wormholes. First, we investigate wormholes and their geometry using the redshift function under various conditions. Subsequently, we discuss the embedding diagram of the upper and lower universe using radial coordinates in two and three-dimensional Euclidean affine space. Three exclusive models are considered for the f(R) theories of gravity,and the radial and tangential pressures are observed. Furthermore, by taking a definite shape function, we observe the behavior of energy conditions. We determine that energy conditions are violated, and their violation is generic and represents the presence of exotic matter. According to Einstein’s field theory, the existence of wormholes is predicated on the occurrence of rare material. Hence, we conclude that our study is more realistic and stable.