This paper investigates the solvability, existence and uniqueness of solutions for a class of nonlinear fractional hybrid differential equations with Hilfer fractional derivative in a weighted normed space. The main result is proved by means of a fixed point theorem due to Dhage. An example to illustrate the results is included.

In this paper, we discuss the performance of applying hybrid spiral dynamic bacterial chemotaxis (HSDBC) optimisation algorithm on an intelligent controller for a differential drive robot. A unicycle class of differential drive robot is utilised to serve as a basis application to evaluate the performance of the HSDBC algorithm. A hybrid fuzzy logic controller is developed and implemented for th...

Formulations of fuzzy integral equations in terms of the Aumann integral do not reflect the behavior of corresponding crisp models. Consequently, they are ill-adapted to describe physical phenomena, even when vagueness and uncertainty are present. A similar situation for fuzzy ODEs has been obviated by interpretation in terms of families of differential inclusions. The paper extends this formal...

This paper focuses on the fuzzy Volterra integro-differential equation of nth order of the second-kind with nonlinear fuzzy kernel and initial values. The derived integral equations are solvable, the solutions of which are unique under certain conditions. The existence and uniqueness of the solutions are investigated in a theorem and an upper boundary is found for solutions. Comparison of the e...

One of the methods for solving definite integrals is modified trapezoid method, which is obtained by using Hermitian interpolation (see e.g. [12]). In this article, we have used modified trapezoid quadrature method and Generalized differential to solve the Fredholm fuzzy integral equations of the second kind. This method leads to solve fuzzy linear system. Finally the proposed method is illustr...

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...

An adaptive fuzzy gain scheduling scheme for robotic arm has been proposed. This paper focus on adaptive fuzzy based tracking and gain controller algorithm for obtaining the joints position relative to the desired trajectory, which drives static and different time variations on the environmental changes. We able to estimate them at any point of time, when t >0 or alternatively, starting from th...

Received 17 September 2011; revised 10 November 2011; accepted 17 November 2011. ———————————————————————————————Abstract In this paper, the fuzzy solution of non-linear fuzzy Volterra integro-differential equation (NFIDE) is approximated. To do this, we define a sequence of fuzzy functions which approximate the fuzzy solution of this type of equations and finally, we estimate upper bound of the...

This paper targets to investigate the numerical solution of -th order fuzzy differential equations with fuzzy environment using Homotopy Perturbation Method (HPM). Triangular fuzzy convex normalized sets are used for the fuzzy parameter and variables. Obtained results are compared with the existing solution depicted in term of plots to show the efficiency of the applied method.