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Nonlocal Cauchy problems for fractional order nonlinear differential systems

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Central European Journal of Physics

Abstract

In this paper, we discuss nonlocal Cauchy problems for fractional order nonlinear differential systems. Firstly, an important matrix associated with fractional order and two functionals are constructed. Further, some sufficient conditions which guarantee such matrix convergent to zero matrix are presented. Secondly, by using three fixed point theorems via the techniques that use convergent to zero matrix and vector norm, some existence results for the solutions of such fractional order nonlinear differential systems are given under different conditions. Finally, some examples are given to illustrate the results.

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Authors and Affiliations

  1. Department of Mathematics, Guizhou Normal College, Guiyang, Guizhou, 550018, P.R. China

    JinRong Wang

  2. Department of Mathematics, Guizhou University, Guiyang, Guizhou, 550025, P.R. China

    JinRong Wang & Xuezhu Li

  3. Department of Mathematics, Xiangtan University, Xiangtan, Hunan, 411105, P.R. China

    Yong Zhou

Authors
  1. JinRong Wang
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  2. Xuezhu Li
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  3. Yong Zhou
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Correspondence to Yong Zhou.

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Wang, J., Li, X. & Zhou, Y. Nonlocal Cauchy problems for fractional order nonlinear differential systems. centr.eur.j.phys. 11, 1399–1413 (2013). https://doi.org/10.2478/s11534-013-0233-1

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  • DOI: https://doi.org/10.2478/s11534-013-0233-1

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