By using an interpolative approach, we recognize the Hardy-Rogers fixed point theorem in the class of metric spaces. The obtained result is supported by some examples. We also give the partial metric case, according to our result.

In the present paper, we use analytical techniques to solve fractional nonlinear differential equations systems that arise in Bergman’s minimal model, used to describe blood glucose and insulin metabolism, after intravenous tolerance testing. We also discuss the stability and uniqueness of the solution.

In this article, we prove some fixed-point theorems in b-dislocated metric space. Thereafter, we propose a simple and efficient solution for a non-linear integral equation and non-linear fractional differential equations of Caputo type by using the technique of fixed point.

In this paper, we aim to obtain fixed-point results by merging the interesting fixed-point theorem of Pata and Suzuki in the framework of complete metric space and to extend these results by involving admissible mapping. After introducing two new contractions, we investigate the existence of a (common) fixed point in these new settings. In addition, we shall consider an integral equation as an application of obtained results.

This chapter presents some new exact solutions corresponding to unsteady magnetohydrodynamic (MHD) flow of Jeffrey fluid in a long porous rectangular duct oscillating parallel to its length. The exact solutions are established by means of the double finite Fourier sine transform (DFFST) and discrete Laplace transform (LT). The series solution of velocity field, associated shear stress and volume flow rate in terms of Fox H-functions, satisfying all imposed initial and boundary conditions, have been obtained. Also, the obtained results are analyzed graphically through various pertinent parameter.