A Fractional Order (FO) ProportionalIntegralDerivative (PID) controller has been proposed in this paper which works on the closed loop error and its fractional derivative and fractional integrator. FOPID is a PID controller whose derivative and integral orders are of fractional rather than integer. The extension of derivative and integral order from integer to fractional order provides more fle...

In this paper, we obtain new sufficient conditions of the existence mild solutions for Hilfer fractional evolution equations in cases that semigroup associated with an almost sectorial operator is compact as well noncompact. Our results improve and extend some recent references.

<p style='text-indent:20px;'>The aim of this paper is to study the calcium profile governed by advection diffusion equation. The mathematical and computational modeling has provided insights understand signalling which depends upon cytosolic concentration. Here model includes important physiological parameters like coefficient, flow velocity etc. fractionalised using Hilfer derivative app...

using the riemann-liouville fractional differintegral operator, the lie theory is reformulated. the fractional poisson bracket over the fractional phase space as 3n state vector is defined to be the fractional lie derivative. its properties are outlined and proved. a theorem for the canonicity of the transformation using the exponential operator is proved. the conservation of its generator is p...