Fractional derivatives provide an excellent tool for the description of memory and hereditary properties of various materials and processes. These characteristics of the fractional derivatives make the fractional-order models more realistic and practical than the classical integer-order models. In recent years, boundary value problems for nonlinear fractional differential equations have been ad...

In this paper, we introduce a high dimensional system of singular fractional differential equations. Using Schauder fixed point theorem, prove an existence result. We also investigate the uniqueness solution using Banach contraction principle. Moreover, study Ulam-Hyers stability and generalized-Ulam-Hyers solutions. Some illustrative examples are presented.

Fractional calculus differentiation and integration of arbitrary order is proved to be an important tool in the modelling of dynamical systems associated with phenomena such as fractal and chaos. In fact, this branch of calculus has found its applications in various disciplines of science and engineering such as mechanics, electricity, chemistry, biology, economics, control theory, signal and i...