Stability of some generalized fractional differential equations in the sense of Ulam-Hyers-Rassias.

In this paper, we investigate the existence and uniqueness of fractional differential equations (FDEs) by using the fixed-point theory (FPT). We discuss also the Ulam-Hyers-Rassias (UHR) stability of some generalized FDEs according to some classical mathematical techniques and the FPT. Finally, two illustrative examples are presented to show the validity of our results.

A New Stabled Relaxation Method for Pricing European Options Under the Time-Fractional Vasicek Model.

Our objective is to solve the time-fractional Vasicek model for European options with a new stabled relaxation method. This new approach is based on the splitting method. Some numerical tests are presented to show the stability and the reliability of our approach with the theory of options.

Some results for a class of two-dimensional fractional hyperbolic differential systems with time delay.

This work deals with the existence and uniqueness of global solution and finite time stability of fractional partial hyperbolic differential systems (FPHDSs). Using the fixed-point approach, the existence and uniqueness of global solution is studied and an estimation of solution is given. Moreover, some sufficient conditions for the finite time stability of FPHDSs are established. Numerical experiments illustrate the Stability result.