Characterization of warped product manifolds through the -curvature tensor with applications to relativity.

We first investigate how the flatness and the symmetry of the -tensor impact both the base manifold and the fiber manifold of a warped product manifold. In both cases, we determine the form of the -tensor on both the fiber and the base manifolds. Additionally, we establish that the fiber manifold is of constant curvature, while the base manifold is Einstein.

High performance computational approach to study model describing reversible two-step enzymatic reaction with time fractional derivative.

Enzyme reactions have numerous applications in diverse disciplines of science like chemistry, biology and biomechanics. In this study, we examine the role and act of enzymes in chemical reactions which is considered in the frame of fractional order model. The proposed model includes system of four equations which are studied via Caputo fractional operator.