Fuzzy differential equations have gained significant attention in recent years due to their ability model complex systems the presence of uncertainty or imprecise information. These find applications various fields, such as biomathematics, horological processes, production inventory models, epidemic fluid and economic investments. The Fisher is one example, which studies dynamics a population w...

In this article, we develop the distributed order fractional hybrid differential equations (DOFHDEs) with linear perturbations involving the fractional Riemann-Liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-Lipschit...

This paper presents an adaptive hybrid fuzzy controller to achieve prescribed tracking performance of fractional order chaotic systems. Depending on plant knowledge and control knowledge, a weighting factor can be adjusted by combining the indirect adaptive fuzzy control effort and the direct fuzzy adaptive control effort. Nonlinear fractional order chaotic response system is fully demonstrated...

In this paper, we apply the concept of Caputo’s H-differentiability, constructed based on the generalized Hukuhara difference, to solve the fuzzy fractional differential equation (FFDE) with uncertainty. This is in contrast to conventional solutions that either require a quantity of fractional derivatives of unknown solution at the initial point (Riemann–Liouville) or a solution with increasing...

  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 pro...

In this paper, we propose the spectral collocation method based on radial basis functions to solve the fractional Bagley-Torvik equation under uncertainty, in the fuzzy Caputo's H-differentiability sense with order ($1< nu < 2$). We define the fuzzy Caputo's H-differentiability sense with order $nu$ ($1< nu < 2$), and employ the collocation RBF method for upper and lower approximate solutions. ...

In this paper, the Caputo time varying singular fractional differential systems with delay and the Riemann-Liouville time varying singular fractional differential systems with delay are considered . By the D− inverse matrix and α − δ function, two fundamental solutions are given. The variation formulae for time varying singular fractional differential systems with delay are obtained. Mathematic...

‎In this article‎, ‎the multi-step conformable fractional differential transform method (MSCDTM) is applied to give approximate solutions of the conformable fractional-order differential systems‎. ‎Moreover‎, ‎we check the stability of conformable fractional-order L\"{u} system with the MSCDTM to demonstrate the efficiency and effectiveness of the proposed procedure.

This paper is concerned with the existence and uniqueness of mild solution to functional fractional fuzzy impulsive differential equations. For the existence and uniqueness we use the Banach fixed point theorem and the nonlinear alternative of Leray-Schauder type.

*Correspondence: [email protected] School of Mathematical Science, Anhui University, Hefei, P.R. China Abstract In this paper, using the theory of q-fractional calculus, we deal with the q-Mittag-Leffler stability of q-fractional differential systems, and based on it, we analyze the direct Lyapunov method of q-fractional differential systems. Several sufficient criteria are established to guaran...