In this paper, a novel problem of observer-based adaptive fuzzy fractional control for fractional order dynamic systems with commensurate orders is investigated; the control scheme is constructed by using the backstepping and adaptive technique. Dynamic surface control method is used to avoid the problem of “explosion of complexity” which is caused by backstepping design process. Fuzzy logic sy...

In this paper, a Bernoulli pseudo-spectral method for solving nonlinear fractional Volterra integro-differential equations is considered. First existence of a unique solution for the problem under study is proved. Then the Caputo fractional derivative and Riemman-Liouville fractional integral properties are employed to derive the new approximate formula for unknown function of the problem....

This paper is concerned with the discretization of the fractional-order differentiator and integrator, which is the foundation of the digital realization of fractional order controller. Firstly, the parameterized Al-Alaoui transform is presented as a general generating function with one variable parameter, which can be adjusted to obtain the commonly used generating functions (e.g. Euler operat...

In this contribution the solution of Fractional Optimal Control Problems (FOCP) by using Orthogonal Collocation Method (OCM) and Multi-objective Optimization Stochastic Fractal Search (MOSFS) algorithm is investigated. For purpose, three classical case studies on engineering are considered. Initially, concentration profiles laccase enzyme production process analyzed to evaluate influence fracti...

Conventional management of debilitating pediatric scar contractures, including hand therapy and surgery, may often be beset by delayed treatment, suboptimal results, and additional surgical morbidity. Ablative fractional laser resurfacing is an emerging adjunctive procedural option for scar contractures because of its promising efficacy and safety profile. However, its use to improve function h...

in this paper, exp-function and (g′/g)expansion methods are presented to derive traveling wave solutions for a class of nonlinear space-time fractional differential equations. as a results, some new exact traveling wave solutions are obtained.

Three approaches of second order mixed type duality are introduced for a nondifferentiable multiobjective fractional programming problem in which the numerator and denominator of objective function contain square root of positive semidefinite quadratic form. Also, the necessary and sufficient conditions of efficient solution for fractional programming are established and a parameterization tech...

When a fractional criterion is to be described by linguistic variables two kinds of approaches are possible: to treat it as a unity (nominator/denominator) and to construct a classic membership function or to aggregate the membership functions separately associated to nominator and denominator respectively. In the paper, two propositions are formulated related to choosing possibilities of aggre...

In this paper, boundary value problems of fractional order are converted into an optimal control problems. Then an approximate solution is constructed from translations and dilations of a B-spline function such that the exact boundary conditions are satisfied. The fractional differential operators are taken in the Riemann-Liouville and Caputo sense. Several example are given and the optimal err...