Approximate analytical solutions of Goursat problem within local fractional operators

Volume 9, Issue 6, pp 4829--4837 http://dx.doi.org/10.22436/jnsa.009.06.118

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Authors

Dumitru Baleanu - Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Ankara, Turkey. Hassan Kamil Jassim - Department of Mathematics, Faculty of Education for Pure Sciences, University of Thi-Qar, Nasiriyah, Iraq. Maysaa Al Qurashi - Department of Mathematics, College of Science, King Saud University, Ryad, Saudi Arabia.

Abstract

The local fractional differential transform method (LFDTM) and local fractional decomposition method (LFDM) are applied to implement the homogeneous and nonhomogeneous Goursat problem involving local fractional derivative operators. The approximate analytical solution of this problem is calculated in form of a series with easily computable components. Examples are studied in order to show the accuracy and reliability of presented methods. We demonstrate that the two approaches are very effective and convenient for finding the analytical solutions of partial differential equations with local fractional derivative operators.

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Keywords

• Goursat problem
• local fractional differential transform method
• local fractional decomposition method
• analytical solutions
• local fractional derivative operators.

MSC

•  26A33
•  35R11
•  74H10

References

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