Integral Means of Univalent Solution for Fractional Differential Equation

Affiliation(s)

School of Mathematical Sciences, Faculty of science and Technology, University Kebangsaan Malaysia, Bangi, Malaysia.

School of Mathematical Sciences, Faculty of science and Technology, University Kebangsaan Malaysia, Bangi, Malaysia.

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.

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.

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.

R. Ibrahim and M. Darus, "Integral Means of Univalent Solution for Fractional Differential Equation,"

References

[1] M. Darus and R. W. Ibrahim, “Radius Estimates of a Subclass of Univalent Functions,” Matematicki Vesnik, Vol. 63, No. 1, 2011, pp. 55-58.

[2] H. M. Srivastava, Y. Ling and G. Bao, “Some Distortion Inequalities Assotiated with the Fractional Drivatives of Analytic and Univalent Functions,” Journal of Inequalities in Pure and Applied Mathematics, Vol. 2, No. 2, 2001, pp. 1-6.

[3] H. M. Srivastava and S. Owa, “Univalent Functions, Fractional Calculus, and Their Applications,” Halsted Press, John Wiley and Sons, New York, 1989.

[4] R. W. Ibrahim and M. Darus, “Subordination and Superordination for Analytic Functions Involving Fractional Integral Operator,” Complex Variables and Elliptic Equations, Vol. 53, No. 11, 2008, pp. 1021-1031. doi:10.1080/17476930802429131

[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

[6] J. E. Littlwood, “On Inequalities in the Theory of Functions,” Proceedings of the London Mathematical Society, Vol. 23, 1925, pp. 481-519. doi:10.1112/plms/s2-23.1.481

[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.

[1] M. Darus and R. W. Ibrahim, “Radius Estimates of a Subclass of Univalent Functions,” Matematicki Vesnik, Vol. 63, No. 1, 2011, pp. 55-58.

[2] H. M. Srivastava, Y. Ling and G. Bao, “Some Distortion Inequalities Assotiated with the Fractional Drivatives of Analytic and Univalent Functions,” Journal of Inequalities in Pure and Applied Mathematics, Vol. 2, No. 2, 2001, pp. 1-6.

[3] H. M. Srivastava and S. Owa, “Univalent Functions, Fractional Calculus, and Their Applications,” Halsted Press, John Wiley and Sons, New York, 1989.

[4] R. W. Ibrahim and M. Darus, “Subordination and Superordination for Analytic Functions Involving Fractional Integral Operator,” Complex Variables and Elliptic Equations, Vol. 53, No. 11, 2008, pp. 1021-1031. doi:10.1080/17476930802429131

[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

[6] J. E. Littlwood, “On Inequalities in the Theory of Functions,” Proceedings of the London Mathematical Society, Vol. 23, 1925, pp. 481-519. doi:10.1112/plms/s2-23.1.481

[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.