Existence and uniqueness of solutions of differential equations of fractional order with integral boundary conditions

Volume 7, Issue 4, pp 246--254 http://dx.doi.org/10.22436/jnsa.007.04.02

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Authors

J. A. Nanware - Department of Mathematics, Shrikrishna Mahavidyalaya, Gunjoti - 413 606, Dist. Osmanabad (M.S), India. D. B. Dhaigude - Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad - 431 004, India.

Abstract

Recently, Wang and Xie [T. Wang, F. Xie, J. Nonlinear Sci. Appl., 1 (2009), 206-212] developed monotone iterative method for Riemann-Liouville fractional differential equations with integral boundary conditions with the strong hypothesis of locally Hölder continuity and obtained existence and uniqueness of a solution for the problem. In this paper, we apply the comparison result without locally Hölder continuity due to Vasundhara Devi to develop monotone iterative method for the problem and obtain existence and uniqueness of a solution of the problem.

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Keywords

• Fractional differential equations
• existence and uniqueness
• lower and upper solutions
• integral boundary conditions.

MSC

•  34A12
•  34C60
•  34A45

References

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