Abstract Fractional order controllers become increasingly popular due to their versatility and superiority in various performances. However, the bottleneck deploying these tools practice is related analog or numerical implementation. Numerical approximations are usually employed which approximation of fractional differintegrator foundation. Generally, following three identical equations always ...

In this article, we study the existence of integral solutions for two classes of fractional order evolution equations with nondensely defined linear operators. First, we consider the nonhomogeneous fractional order evolution equation and obtain its integral solution by Laplace transform and probability density function. Subsequently, based on the form of integral solution for nonhomogeneous fra...

Classical and anomalous diffusion equations employ integer derivatives, fractional derivatives, and other pseudodifferential operators in space. In this paper we show that replacing the integer time derivative by a fractional derivative subordinates the original stochastic solution to an inverse stable subordinator process whose probability distributions are Mittag-Leffler type. This leads to e...