A boundary value problem of fractional order at resonance.
A general method to solve fractional differential equations on
A method to solve an equation with left and right fractional derivatives
A new characteristic property of Mittag-Leffler functions and fractional cosine functions
A new characteristic property of the Mittag-Leffler function with 1 < α < 2 is deduced. Motivated by this property, a new notion, named α-order cosine function, is developed. It is proved that an α-order cosine function is associated with a solution operator of an α-order abstract Cauchy problem. Consequently, an α-order abstract Cauchy problem is well-posed if and only if its coefficient operator generates a unique α-order cosine function.
A novel control method for integer orders chaos systems via fractional-order derivative.
A numerical method for solution of semidifferential equations
A Poster about the Old History of Fractional Calculus
MSC 2010: 26A33, 05C72, 33E12, 34A08, 34K37, 35R11, 60G22The fractional calculus (FC) is an area of intensive research and development. In a previous paper and poster we tried to exhibit its recent state, surveying the period of 1966-2010. The poster accompanying the present note illustrates the major contributions during the period 1695-1970, the "old history" of FC.
A Poster about the Recent History of Fractional Calculus
MSC 2010: 26A33, 05C72, 33E12, 34A08, 34K37, 35R11, 60G22In the last decades fractional calculus became an area of intense re-search and development. The accompanying poster illustrates the major contributions during the period 1966-2010.
A problem on the zeros of the Mittag-Leffler function and the spectrum of a fractional-order differential operator.
A refinement of quasilinearization method for Caputo's sense fractional-order differential equations.
A theory of linear differential equations with fractional derivatives
Almost automorphic solutions to abstract fractional differential equations.
An analysis of the stability boundary for a linear fractional difference system
This paper deals with basic stability properties of a two-term linear autonomous fractional difference system involving the Riemann-Liouville difference. In particular, we focus on the case when eigenvalues of the system matrix lie on a boundary curve separating asymptotic stability and unstability regions. This issue was posed as an open problem in the paper J. Čermák, T. Kisela, and L. Nechvátal (2013). Thus, the paper completes the stability analysis of the corresponding fractional difference...
An equation in the left and right fractional derivatives of the same order
An existence result for nonlinear fractional differential equations on Banach spaces.
An existence theorem for fractional hybrid differential inclusions of Hadamard type
This paper studies the existence of solutions for fractional hybrid differential inclusions of Hadamard type by using a fixed point theorem due to Dhage. The main result is illustrated with the aid of an example.
Asymptotically linear solutions for some linear fractional differential equations.
Boundary value problems for Hadamard-Caputo implicit fractional differential inclusions with nonlocal conditions
In this paper, the authors establish sufficient conditions for the existence of solutions to implicit fractional differential inclusions with nonlocal conditions. Both of the cases of convex and nonconvex valued right hand sides are considered.
Chaos synchronization of a fractional nonautonomous system
In this paper we investigate the dynamic behavior of a nonautonomous fractional-order biological system.With the stability criterion of active nonlinear fractional systems, the synchronization of the studied chaotic system is obtained. On the other hand, using a Phase-Locked-Loop (PLL) analogy we synchronize the same system. The numerical results demonstrate the effectiveness of the proposed methods.
Conflict-Controlled Processes Involving Fractional Differential Equations with Impulses
MSC 2010: 34A08, 34A37, 49N70Here we investigate a problem of approaching terminal (target) set by a system of impulse differential equations of fractional order in the sense of Caputo. The system is under control of two players pursuing opposite goals. The first player tries to bring the trajectory of the system to the terminal set in the shortest time, whereas the second player tries to maximally put off the instant when the trajectory hits the set, or even avoid this meeting at all. We derive...