This paper proposes two novel fuzzy fractional PID structures. The tuning of the fuzzy fractional controllers is based on the prior knowledge of fractional-order control tuning rules. The digital implementation of these controllers is also investigated. The effectiveness and robustness of the proposed tuning methodology is illustrated through its application on a fractional-order plant. The sim...

In this paper, multi-objective optimization is used for Pareto optimum design of fuzzy fractional-order PID controllers for plants with parametric uncertainties. Two conflicting objective functions have been used in Pareto design of the fuzzy fractional-order PID controller. The results clearly show that an effective trade-off can be compromisingly achieved among the different fuzzy fractional-...

in this paper, we present a fractional mathematical model of a one-dimensional phase phase change problem (stefan problem) with latent heat a power function of position. this model includes space-time fractional derivatives in caputo sense and time dependent surface heat flux. an approximate solution of this model is obtained by optimal homotopy asymptotic method (oham) to find an approximate s...

A novel fractional order (FO) fuzzy Proportional-Integral-Derivative (PID) controller has been proposed in this paper which works on the closed loop error and its fractional derivative as the input and has a fractional integrator in its output. The fractional order differ-integrations in the proposed fuzzy logic controller (FLC) are kept as design variables along with the input-output scaling f...

This paper presents a fuzzy goal programming (GP) procedure for solving a multiobjective linear plus linear fractional programming problem. In the proposed approach GP model for achievement of the highest membership value of each of fuzzy goal defined for the linear plus linear fractional objectives is formulated. In the solution process, the method of variable change on the underand overdeviat...

This paper deals with a solution procedure for solving linear fuzzy fractional transportation problem (LFFTP) which is a special type of linear fuzzy fractional programming problem (LFFPP). Fuzzy version of improved Vogel’s approximation method and Fuzzy version of Modi method are used to obtain the fuzzy optimal solution to the given LFFTP by without reformulating the original problem into an ...

In this paper, the improved Euler method is used for solving hybrid fuzzy fractional differential equations (HFFDE) of order q ∈ (0,1) under Caputo-type fuzzy fractional derivatives. This method is based on the fractional Euler method and generalized Taylor’s formula. The accuracy and efficiency of the proposed method is demonstrated by solving numerical examples.

In this paper we use the fuzzy Caputo derivatives under generalized Hukuhara difference to introduce fuzzy fractional Volterra-Fredholm integro-differential equations and prove the existence and uniqueness of the solutions for this class of fractional equations.

abstract it is the purpose of this article to introduce a linear approximation technique for solving a fractional chance constrained programming (cc) problem. for this purpose, a fuzzy goal programming model of the equivalent deterministic form of the fractional chance constrained programming is provided and then the process of defuzzification and linearization of the problem is started. a samp...

At the end of the 19th century Liouville and Riemann introduced the notion of a fractional-order derivative, and in the latter half of the 20th century the concept of the so-called Grünewald-Letnikov fractional-order discrete difference has been put forward. In the paper a predictive controller for MIMO fractional-order discrete-time systems is proposed, and then the concept is extended to nonl...