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Integral Means of Univalent Solution for Fractional Differential Equation

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DOI: 10.4236/am.2012.36091    3,214 Downloads   5,373 Views  

ABSTRACT

By employing the Srivastava-Owa fractional operators, we consider a class of fractional differential equation in the unit disk. The existence of the univalent solution is founded by using the Schauder fixed point theorem while the uniqueness is obtained by using the Banach fixed point theorem. Moreover, the integral mean of these solutions is studied by applying the concept of the subordination.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

R. Ibrahim and M. Darus, "Integral Means of Univalent Solution for Fractional Differential Equation," Applied Mathematics, Vol. 3 No. 6, 2012, pp. 590-593. doi: 10.4236/am.2012.36091.

References

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[3] H. M. Srivastava and S. Owa, “Univalent Functions, Fractional Calculus, and Their Applications,” Halsted Press, John Wiley and Sons, New York, 1989.
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[5] R. W. Ibrahim and M. Darus, “Subordination and Superordination for Univalent Solutions for Fractional Differential Equations,” Journal of Mathematical Analysis and Applications, Vol. 345, No. 2, 2008, pp. 871-879. doi:10.1016/j.jmaa.2008.05.017
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[7] R. W. Ibrahim and M. Darus, “Integral Means of Univalent Solution for Fractional Equation in Complex Domain,” Acta Universitatis Apulensis, Vol. 23, 2010, pp. 1-8.

  
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