Stability Theory Corresponds to the Deformable Derivative

Abstract

The fractional and generalized derivatives have gained more attention due to their broad and diverse applications. They offer great tool sets for modelling systems that exhibit dynamics with memory and heredity. A new operator was recently introduced, namely deformable derivative, which is capable of fractionalized derivatives. Stability theory is crucial in many areas of science and engineering. Stability theory shows how the solutions of differential equations behave under small perturbation. This communication addresses the relationship of stability theory with deformable derivative. Some basic properties of the new operator are proved and studied. Stability of systems of differential equations formed with the help of this operator is studied.