A charged analogue of Schwarzschild's interior solution has been derived by considering the non-gravitational energy density to be constant along with a special choice of electric intensity. The charged fluid sphere so obtained is seen to be more general than that of P.S. Florides and joins smoothly with the Reissner-Nordström metric at the pressure-free interface. Also the new charged fluid sphere is capable of representing a superdense star with surface density of 2 × 10 14 g cm −3 which can occupy maximum mass 1.502408 times the solar mass. In the process of deriving the solution, the authors have also come across A. L. Mehra's gaseous charged fluid model which is found to be unphysical as it has negative pressure at least at the center of the model.

This paper is concerned with the existence and uniqueness of a mild solution of a semilinear fractional-order functional evolution differential equation with the infinite delay and impulsive effects. The existence and uniqueness of a mild solution is established using a solution operator and the classical fixed-point theorems.

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In this article, we develop a higher order numerical approximation for time dependent singularly perturbed differential‐difference convection‐diffusion equations. A priori bounds on the exact solution and its derivatives, which are useful for the error analysis of the numerical method are given. We approximate the retarded terms of the model problem using Taylor's series expansion and the resulting time‐dependent singularly perturbed problem is discretized by the implicit Euler scheme on uniform mesh in time direction and a special hybrid finite difference scheme on piecewise uniform Shishkin mesh in spatial direction. We first prove that the proposed numerical discretization is uniformly convergent of O ( Δ t + N − 2 false( ln ⁡ N false) 2 ) , where Δ t and N denote the time step and number of mesh‐intervals in space, respectively. After that we design a Richardson extrapolation scheme to increase the order of convergence in time direction and then the new scheme is proved to be uniformly convergent of O ( Δ t 2 + N − 2 false( ln ⁡ N false) 2 ) . Some numerical tests are performed to illustrate the high‐order accuracy and parameter uniform convergence obtained with the proposed numerical methods.

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