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...

*Correspondence: [email protected]; [email protected] 1School of Sciences, Nanchang University, Nanchang, 330031, P.R. China 2Numerical Simulation and High-Performance Computing Laboratory, Nanchang University, Nanchang, 330031, P.R. China Abstract In this paper, a reaction-diffusion trimolecular biochemical model with autocatalysis and fractional-order derivative is proposed. We esta...

in this paper, a new numerical method for solving fractional optimal control problems (focps) is presented. the fractional derivative in the dynamic system is described in the caputo sense. the method is based upon biorthogonal cubic hermite spline multiwavelets approxima-tions. the properties of biorthogonal multiwavelets are first given. the operational matrix of fractional riemann-lioville i...

Abstract. This paper deals with the solution of unified fractional reactiondiffusion 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 numerical computation. On account of the most general character of the derived results, numerous results on fractional reaction, fractional diffusi...

Biochemical reaction systems may be viewed as discrete event processes characterized by a number of states and state transitions. These systems may be modeled as state transition systems with transitions representing individual reaction events. Since they often involve a large number of interactions, it can be difficult to construct such a model for a system, and since the resulting state-level...

Reaction systems, a formalism describing biochemical reactions in terms of sets of reactants, inhibitors, and products, are known to have a PSPACE-complete configuration reachability problem. We show that the complexity of the problem remains unchanged even for some classes of resource-bounded reaction systems, where we disallow either inhibitors or reactants. We also prove that the complexity ...