The main concern of this paper is to investigate the existence and uniqueness a fuzzy neutral impulsive stochastic differential system with Caputo fractional order driven by Brownian motion using numbers bounded ν-level intervals that are convex, normal upper-semicontinuous. Fuzzy Itô process, Grönwall’s inequality Banach fixed-point theorem employed probe local global existence. An analytical ...

We consider a fractional generalization of Hamiltonian and gradient systems. We use differential forms and exterior derivatives of fractional orders. We derive fractional generalization of Helmholtz conditions for phase space. Examples of fractional gradient and Hamiltonian systems are considered. The stationary states for these systems are derived. PACS numbers: 45.20.−d, 05.45.−a

Abstract -In this paper, the problem of H∞ filtering design is studied for nonlinear sampled-data systems using the Takagi-Sugeno (T-S) fuzzy model approach. Traditionally, the sufficient conditions for the existence of such H∞ filter are characterized in terms of the solution of a differential Hamilton-Jacobi inequality with jumps, which is equivalent to solving the partial differential inequa...

In this article, Multi-step Differential Transform Method (MsDTM) extends to give approximate and analytical solutions of nonlinear fractional order ordinary differential equation systems such as a Newton-Leipnik chaotic systems. The solutions of numerical obtained from proposed method reveal that the approach is very effective and convenient when apzplied to systems of fractional differential ...

The fuzzy approach has undergone a profound structural transformation in the past few decades. Numerous studies have been undertaken to explain fuzzy approach for linear and nonlinear programs. While, the findings in earlier studies have been conflicting, recent studies of competitive situations indicate that fractional programming problem has a positive impact on comparative scenario. We propo...

We apply the Radu–Miheţ method derived from an alternative fixed-point theorem with a class of matrix-valued fuzzy controllers to approximate fractional Volterra integro-differential equation ψ-Hilfer derivative in k-normed spaces obtain approximation for this type equation.

In this paper, we consider two new uniqueness results for fuzzy fractional differential equations (FFDEs) involving Riemann-Liouville generalized H-differentiability with the Nagumo-type condition and the Krasnoselskii-Krein-type condition. To this purpose, the equivalent integral forms of FFDEs are determined and then these are used to study the convergence of the Picard successive approximati...