In the recent paper Communications in Nonlinear Science and Numerical Simulation. Vol.18. No.11. (2013) 2945-2948, it was demonstrated that a violation of the Leibniz rule is a characteristic property of derivatives of non-integer orders. It was proved that all fractional derivatives Dα, which satisfy the Leibniz rule Dα(fg) = (Dαf) g+ f (Dαg), should have the integer order α = 1, i.e. fraction...

We study the burden of the HIV viremia and of treatment efficacy in the severity of the patterns of the HIV/HCV coinfection. For this, we derive a simple non-integer-order (fractional-order) model for the coinfection dynamics. Fractional-order models have been proved in the literature to provide good fits to real data from patients suffering from several diseases, such as HIV, dengue fever, and...

In this paper, we study a new operational numerical method for hybrid fuzzy fractional differential equations by using of the hybrid functions under generalized Caputo- type fuzzy fractional derivative. Solving two examples of hybrid fuzzy fractional differential equations illustrate the method.

This paper presents an analytical technique for the analysis of a stochastic dynamic system whose damping behavior is described by a fractional derivative of order 1/2. In this approach, an eigenvector expansion method proposed by Suarez and Shokooh is used to obtain the response of the system. The properties of Laplace transforms of convolution integrals are used to write a set of general Duha...

‎in this paper‎, ‎we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation‎. ‎by applying kranoselskii`s fixed--point theorem in a cone‎, ‎first we prove the existence of solutions of an auxiliary bvp formulated by truncating the response function‎. ‎then the arzela--ascoli theorem is used to take $c^1$ ...

The given article is devoted to presentation of some results regarding existence and uniqueness solution a fractional order model that addressing the effect immigration on transmission dynamics population model. Further, in view this investigation have been checked recent pandemic known as Corona virus COVID-19. concerned established by using fixed point theory approach. After qualitative analy...

Abstract: In this paper, we studied the numerical solution of a time-fractional Korteweg–de Vries (KdV) equation with new generalized fractional derivative proposed recently. The fractional derivative employed in this paper was defined in Caputo sense and contained a scale function and a weight function. A finite difference/collocation scheme based on Jacobi–Gauss–Lobatto (JGL) nodes was applie...