The time fractional heat conduction in an infinite plate of finite thickness, when both faces are subjected to boundary conditions of second kind, has been studied. The time fractional heat conduction equation is used, when attempting to describe transport process with long memory, where the rate of heat conduction is inconsistent with the classical Brownian motion. The stability and convergenc...

In this paper, we consider the fractional Laplacian −(−∆)α/2 on an open subset in R with zero exterior condition. We establish sharp two-sided estimates for the heat kernel of such Dirichlet fractional Laplacian in C open sets. This heat kernel is also the transition density of a rotationally symmetric α-stable process killed upon leaving a C open set. Our results are the first sharp two-sided ...

A model of fractional-order of thermoelasticity is applied to study a 2D problem of mode-I crack in a fibre-reinforced thermal environment. The crack is under prescribed distributions of heat and pressure. The normal mode analysis is applied to deduce exact formulae for displacements, stresses, and temperature. Variations of field quantities with the axial direction are illustrated graphically....

This paper deals with chaos synchronization between two different uncertain fractional order chaotic systems based on adaptive fuzzy sliding mode control (AFSMC). With the definition of fractional derivatives and integrals, a fuzzy Lyapunov synthesis approach is proposed to tune free parameters of the adaptive fuzzy controller on line by output feedback control law and adaptive law. Moreover, c...

In this paper, a new method of predictive control is presented. In this approach, a well-known method of predictive functional control is combined with fuzzy model of the process. The prediction is based on fuzzy model given in the form of Takagi–Sugeno (T–S) type. The proposed fuzzy predictive control has been evaluated by implementation on heat-exchanger plant, which exhibits a strong nonline...

In this paper, we study a particular type of convex fractional programming problem and its dual under fuzzy environment. We present appropriate duality results for a fuzzy environment using aspiration level approach. This study use linear membership functions to represent fulfillment of the decision maker’s degree of satisfaction.

This paper addresses complex, variable-order fractional derivatives, enlarging the definitions for the real case. Implementations combining discretised Crone approximations using fuzzy logic and interpolation are also addressed.

We study a fuzzy fractional differential equation (FFDE) and present its solution using Zadeh's extension principle. The proposed study extends the case of fuzzy differential equations of integer order. We also propose a numerical method to approximate the solution of FFDEs. To solve nonlinear problems, the proposed numerical method is then incorporated into an unconstrained optimisation techni...

In this paper, the researchers present a multi-objective linear fractional inventory model using fuzzy programming. The proposed method in this paper is applied to a problem with two objective functions. The resulted fuzzy model is transformed into an ordinary linear programming. The implementation of the developing model presented in this paper is demonstrated through the use of some numerical...