We propose second-order implicit-explicit (IMEX) time-stepping schemes for nonlinear fractional differential equations with fractional order 0 < β < 1. From the known structure of the nonsmooth solution and by introducing corresponding correction terms, we can obtain uniformly second-order accuracy from these schemes. We prove the convergence and linear stability of the proposed schemes. Numeri...

Comparison results of the nonlinear scalar Riemann-Liouville fractional differential equation of order q, 0 < q ≤ 1, are presented without requiring Hölder continuity assumption. Monotone method is developed for finite systems of fractional differential equations of order q, using coupled upper and lower solutions. Existence of minimal and maximal solutions of the nonlinear fractional different...

this paper presents a computational method for solving two types of integro-differential equations, system of nonlinear high order volterra-fredholm integro-differential equation(vfides) and nonlinear fractional order integro-differential equations. our tools for this aims is operational matrices of integration and fractional integration. by this method the given problems reduce to solve a syst...

This paper presents a novel adaptive fuzzy logic controller (FLC) equipped with an adaptive algorithm to achieve synchronization performance for fractional chaotic systems. By introducing the fuzzy control design and robustness tracking approach, a desired synchronization error can be attenuated to a prescribed level, even in the presence of the high level of uncertainties and noisy training da...

Nowadays in the complicated systems, design of proper and implementable controller has a most importance. With respect to ability of fractional order systems in complicated systems identification as a first order fractional system with time delay, usage of fractional order PID has a proper result. From one side flexibility of fractional calculus than integer order has been topics of interest to...

in recent years, soft computing methods have generated a large research interest. the synthesis of the fuzzy logic and the evolutionary algorithms is one of these methods. a particular evolutionary algorithm (ea) is differential evolution (de). as for any ea, de algorithm also requires parameters tuning to achieve desirable performance. in this paper tuning the perturbation factor vector of de ...

Fractional differential equations have been of great interest recently. This is because of both the intensive development of the theory of fractional calculus itself and the applications of such constructions in various scientific fields such as physics, mechanics, chemistry, engineering, etc. Differential equations with impulsive effects arising from the real world describe the dyn...