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Nonlocal Cauchy problems for fractional order nonlinear differential systems

100%
Wang J., Li X., Zhou Y.
Open Physics
|
2013
|
vol. 11
|
issue 10
1399-1413
EN
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.
2
Content available remote

Existence of solutions for sequential fractional differential equations with four-point nonlocal fractional integral boundary conditions

100%
Ahmad B., Alsaedi A., Al-Hutami H.
Open Physics
|
2013
|
vol. 11
|
issue 10
1487-1493
EN
This paper investigates the existence of solutions for a nonlinear boundary value problem of sequential fractional differential equations with four-point nonlocal Riemann-Liouville type fractional integral boundary conditions. We apply Banach’s contraction principle and Krasnoselskii’s fixed point theorem to establish the existence of results. Some illustrative examples are also presented.
3
Content available remote

Existence and approximation of solutions of fractional order iterative differential equations

100%
Deng J., Wang J.
Open Physics
|
2013
|
vol. 11
|
issue 10
1377-1386
EN
In this paper, we investigate existence and approximation of solutions of fractional order iterative differential equations by virtue of nonexpansive mappings, fractional calculus and fixed point methods. Three existence theorems as well as convergence theorems for a fixed point iterative method designed to approximate these solutions are obtained in two different work spaces via Chebyshev’s norm, Bielecki’s norm and β norm. Finally, an example is given to illustrate the obtained results.
4
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Existence, uniqueness and limit property of solutions to quadratic Erdélyi-Kober type integral equations of fractional order

100%
Wang J., Zhu C., Fečkan M.
Open Physics
|
2013
|
vol. 11
|
issue 6
779-791
EN
In this paper, we apply certain measure of noncompactness and fixed point theorem of Darbo type to derive the existence and limit property of solutions to quadratic Erdélyi-Kober type integral equations of fractional order with three parameters. Moreover, we also present the uniqueness and another existence results of the solutions to the above equations. Finally, two examples are given to illustrate the obtained results.
5
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Positive fractional 2D hybrid linear systems

72%
Kaczorek T.
|
2008
|
vol. 56
|
issue 3
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