A Class of Volterra-Fredholm Difference Inequality with Weakly Singularity in Engineering

Wu Sheng Wang; Zong Yi Hou

doi:10.4028/www.scientific.net/AMM.571-572.139

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 571-572A Class of Volterra-Fredholm Difference Inequality...

A Class of Volterra-Fredholm Difference Inequality with Weakly Singularity in Engineering

Abstract:

In this paper, we discuss a class of new Volterra-Fredholm weakly singular difference inequality. The explicit bounds for the unknown functions are given clearly by discrete Jensen inequality, Cauchy-Schwarz inequality, Gamma function, change of variable, the mean-value theorem for integrals and amplification method. The derived results can be applied in the study of fractional difference equations in engineering.

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Periodical:

Applied Mechanics and Materials (Volumes 571-572)

Pages:

139-142

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.571-572.139

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Online since:

June 2014

Authors:

Wu Sheng Wang*, Zong Yi Hou

Keywords:

Analysis Technique, Difference Inequality, Estimation, Gamma Function, Singular

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References

[1] T. H. Gronwall: Ann Math. vol. 20(1919), p.292.

Google Scholar

[2] R. Bellman: Duke Mathematical Journal, Vol. 10(1943) , p.643.

Google Scholar

[3] S. Sugiyama: Bull. Sci. Engr. Research Lab. Waseda Univ. vol. 45(1969), p.140.

Google Scholar

[4] M. Kuczma: An introduction to the theory of functional equations and inequalities: Cauchy's equation and Jensen's inequality (University of Katowice, Katowice, 1985).

Google Scholar

[5] M. Medved: J. Math. Anal. Appl. Vol. 214(1997) , p.349.

Google Scholar

[6] I. Podlubny: Fractional Differential Equations (Academic Press, New York, 1999).

Google Scholar

[7] Q.H. Ma and E. H. Yang: Acta Math Appl Sin. Vol. 25(2002) , p.505.

Google Scholar

[8] E. H. Yang, Q. H. Ma and M. C. Tan: J. Jinan Univ. Vol. 28(1) (2007), p.1.

Google Scholar

[9] K. Zheng, H. Wang and C. Guo: Advances in Difference Equations Vol. 2013 (2013), Article (239).

Google Scholar