Related papers: An efficient analytical scheme for fuzzy conformab…
This paper concentrates on the study of the decentralized fuzzy control method for a class of fractional-order interconnected systems with unknown control directions. To overcome the difficulties caused by the multiple unknown control…
We give a unified interpretation of confluences, contiguity relations and Katz's middle convolutions for linear ordinary differential equations with polynomial coefficients and their generalization to partial differential equations. The…
Fractional differential equations model processes with memory effects, providing a realistic perspective on complex systems. We examine time-delayed differential equations, discussing first-order and fractional Caputo time-delayed…
We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the…
Duhamel's principle reduces the Cauchy problem for an inhomogeneous partial differential equation to the corresponding homogeneous problem. In the fractional-order setting, the classical principle does not apply directly because fractional…
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…
In this paper, we define generalized Hukuhara diamond-alpha integral for fuzzy functions on time scales and obtain some of its fundamental properties and also we establish the relationship between diamond-alpha differentiation and…
In this article, we deal with the efficient computation of the Wright function in the cases of interest for the expression of solutions of some fractional differential equations. The proposed algorithm is based on the inversion of the…
Based on the continuous time random walk, we derive the Fokker-Planck equations with Caputo-Fabrizio fractional derivative, which can effectively model a variety of physical phenomena, especially, the material heterogeneities and structures…
This paper deals with the investigation of a closed form solution of a generalized fractional reaction-diffusion equation. The solution of the proposed problem is developed in a compact form in terms of the H-function by the application of…
In view of the usefulness and importance of the kinetic equation in certain physical problems, the authors derive the explicit solution of a fractional kinetic equation of general character, that unifies and extends earlier results.…
In this study the general formula for differential and integral operations of fractional calculus via fractal operators by the method of cumulative diminution and cumulative growth is obtained. The under lying mechanism in the success of…
A numerical method to solve the fractional diffusion equation, which could also be easily extended to many other fractional dynamics equations, is considered. These fractional equations have been proposed in order to describe anomalous…
The existing fractional grey prediction models mainly use discrete fractional-order difference and accumulation, but in the actual modeling, continuous fractional-order calculus has been proved to have many excellent properties, such as…
In this paper, we present a new derivative via the Laplace transform. The Laplace transform leads to a natural form of the fractional derivative which is equivalent to a Riemann-Liouville derivative with fixed terminal point. We first…
This paper deals with the solution of unified fractional reaction-diffusion systems. The results are obtained in compact and elegant forms in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for…
We consider fractional directional derivatives and establish some connection with stable densities. Solutions to advection equations involving fractional directional derivatives are presented and some properties investigated. In particular…
We introduce a fractional calculus on time scales using the theory of delta (or nabla) dynamic equations. The basic notions of fractional order integral and fractional order derivative on an arbitrary time scale are proposed, using the…
A natural way to model dynamic systems under uncertainty is to use fuzzy boundary value problems (FBVPs) and related uncertain systems. In this paper we use fuzzy Laplace transform to find the solution of two-point boundary value under…
We prove necessary optimality conditions of Pontryagin type for a class of fuzzy fractional optimal control problems with the fuzzy fractional derivative described in the Caputo sense. The new results are illustrated by computing the…