The space-time-fractional diffusion equation with the Caputo time-fractional derivative and Riesz fractional Laplacian is considered in the case of axial symmetry. Mass absorption (mass release) is described by a source term proportional to concentration. The integral transform technique is used. Different particular cases of the solution are studied. The numerical results are illustrated graph...

This paper presents a numerical scheme for dynamic nalysis of mechanical systems subjected to damping forces which are proportional to fractional derivatives of displacements. In this scheme, a fractional differential equation governing the dynamic of a system is transformed into a set of differential equations with no fractional derivative terms. Using Laguerre integral formula, this set is co...

The concept of automatic generation control has an immense role in providing quality power interconnected system. To obtain by controlling the oscillations frequency and tie-line power, a proper controller design is necessary. So, innovative endeavor been undertaken to enforce two-stage with amalgamation proportional-derivative filter (PDN) (integer-order) fractional order integral-derivative (...

Nature inspired algorithms are the most popular and robust algorithms for the optimization of the real world problems like pitch control of an aircraft system. This paper introduces Bat algorithm and Differential Evolution technique for the multi-objective optimization based designing of the fractional order PID (FOPID) and integer order PID controllers. The optimized values obtained from the t...

The Proportional-Integral-Derivative Controller is widely used in industries for process control applications. Fractional-order PID controllers are known to outperform their integer-order counterparts. In this paper, we propose a new technique of fractional-order PID controller synthesis based on peak overshoot and rise-time specifications. Our approach is to construct an objective function, th...