Real-time robust adaptive fuzzy fractional-order control of electrically driven flexible-joint robots has been addressed in this paper. Two important practical situations have been considered: the fact that robot actuators have limited voltage, and the fact that current signals are contaminated with noise. Through of a novel voltage-based fractional order control for an integer-order dynamical ...

In this paper, we consider some boundary value problems (BVP) for fractional order partial differential equations ‎(FPDE)‎ with non-local boundary conditions. The solutions of these problems are presented as series solutions analytically via modified Mittag-Leffler functions. These functions have been modified by authors such that their derivatives are invariant with respect to fractional deriv...

The fractional parts of the Bernoulli numbers are dense in the interval (0, 1). For every positive integer k, the set of all m for which B 2. has the same fractional part as B 21 has positive asymptotic density .

Abstract As is well known, poly-Bernoulli polynomials are defined in terms of polylogarithm functions. Recently, as degenerate versions such functions and polynomials, were introduced by means the functions, some their properties investigated. The aim this paper to further study using three formulas coming from recently developed ‘ λ -umbral calculus’. In more detail, among other things, we rep...

In this paper, a computational intelligence method is used for the solution of fractional optimal control problems (FOCP)'s with equality and inequality constraints. According to the Ponteryagin minimum principle (PMP) for FOCP with fractional derivative in the Riemann- Liouville sense and by constructing a suitable error function, we define an unconstrained minimization problem. In the optimiz...

In this paper, the problem under consideration is multiobjective non-linear fractional programming problem involving semilocally convex and related functions. We have discussed the interrelation between the solution sets involving properly efficient solutions of multiobjective fractional programming and corresponding scalar fractional programming problem. Necessary and sufficient optimality...