Solvability for a couple system of nonlinear fractional differential equations in a Banach space

Liang, Jun‐Hong; Liu, Zhenhai; Wang, Xuhuan

doi:10.2478/s13540-013-0004-0

Cited by 27 publications

(13 citation statements)

References 23 publications

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“…For more history and basic results on fractional calculus theory, one can see monograph [1][2][3][4][5][6][7][8] and the references therein. Many researchers studied Cauchy problem and long time behavior for nonlinear fractional differential equations and obtained many interesting results by using all kinds of fixed point theorems (see [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]). …”

Section: Introductionmentioning

confidence: 99%

Cauchy problem for nonlinear fractional differential equations with positive constant coefficient

Shan

Wang

2015

J. Appl. Math. Comput.

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In this paper, we consider a Cauchy problem for nonlinear fractional differential equation with constant coefficient λ > 0 of the type:We present monotonicity and continuity of two-parameter Mittag-Leffler function E α,β (z) for z > 0. By using monotonicity, continuity, asymptotic properties of E α,β (z) for z > 0 and fixed point theorems, we obtain existence of solution. Finally, two examples are given to illustrate our theoretical results.

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Section: Introductionmentioning

confidence: 99%

Cauchy problem for nonlinear fractional differential equations with positive constant coefficient

Shan

Wang

2015

J. Appl. Math. Comput.

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“…For example, flocking movement and food searching by means of the individual secretions and microbial, submarine underwater robots in the bottom of the sea with a large number of microorganisms and viscous substances, unmanned aerial vehicles running in the complex space environment [19]. Fractionalorder dynamics and control have provided many comprehensive results of recent advances in the areas of linesr/nonlinear dynamics with analytical, numerical, and experimental methods [9,1,15,13]. Motivated by the broad application of coordination algorithms in multi-agent systems and the fact that many practical systems demonstrated fractional-order dynamics, the distributed coordination of networked fractional-order systems will be studied in this paper.…”

Section: Introductionmentioning

confidence: 99%

Distributed coordination of fractional order multi-agent systems with communication delays

Yang

Zhu

Cao

2013

fcaa

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Because of the complexity of the practical environments, many distributed multi-agent systems can not be illustrated with the integer-order dynamics and can only be described with the fractional-order dynamics. Under the connected network with directed weighted topologies, the dynamical characteristics of agents with fractional-order derivative operator is analyzed in this paper. Applying the Laplace transform and frequency domain theory of the fractional-order operator, the distributed coordination of fractional-order multi-agent systems (FOMAS) with communication delays is studied, and a critical value of time delay is obtained to ensure the consensus of FOMAS. Since the integer-order model is a special case of fractional-order model, the extended results in this paper are in accordance with that of the integer-order model. Finally, numerical examples are provided to verify our results.MSC 2010 : Primary 34K37; Secondary 68T42, 93C85

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“…With this advantage, fractional-order models have become more realistic and practical than the corresponding classical integer-order models. For some recent development on the topic, see [1], [2], [4], [5], [6], [7], [8], [9], [10], [11], [12], [14], [17], and the references therein. The study of coupled systems of fractional order differential equations is also very significant as such systems appear in a variety of problems of applied nature, especially in biosciences.…”

Section: Introductionmentioning

confidence: 99%

A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations

Ahmad

Ntouyas

2014

fcaa

130

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This paper is concerned with the existence and uniqueness of solutions for a coupled system of Hadamard type fractional differential equations and integral boundary conditions. We emphasize that much work on fractional boundary value problems involves either Riemann-Liouville or Caputo type fractional differential equations. In the present work, we have considered a new problem which deals with a system of Hadamard differential equations and Hadamard type integral boundary conditions. The existence of solutions is derived from Leray-Schauder's alternative, whereas the uniqueness of solution is established by Banach's contraction principle. An illustrative example is also included.MSC 2010 : Primary 34A08; Secondary 34A12, 34B15

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Solvability for a couple system of nonlinear fractional differential equations in a Banach space

Cited by 27 publications

References 23 publications

Cauchy problem for nonlinear fractional differential equations with positive constant coefficient

Cauchy problem for nonlinear fractional differential equations with positive constant coefficient

Distributed coordination of fractional order multi-agent systems with communication delays

A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations

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