Fractional Solutions of the Associated Legendre Equation

Year 2016, , 0 - 0, 29.06.2016

Ökkeş Öztürk

https://doi.org/10.17798/beufen.63369

Abstract

Fractional calculus and its generalizations are used for the solutions of some classes of linear ordinary and partial differential equations of the second and higher orders and fractional differential equations. In this paper, our aim is that obtaining fractional solutions of the associated Legendre equation via N-fractional calculus operator  method

References

• Podlubny I, 1999. Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, Methods of Their Solution and Some of Their Applications. Academic Press. USA.
• Miller K, Ross B, 1993. An Introduction to the Fractional Calculus and Fractional Differential Equations. John Wiley and Sons. USA.
• Oldham K, Spanier J, 1974. The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order. Academic Press. USA.
• Bas E, Metin F, 2013. Fractional Singular Sturm-Liouville Operator for Coulomb Potential. Advances in Difference Equation, 2013 (300): 13 pages.
• Bas E, 2013. Fundamental Spectral Theory of Fractional Singular Sturm-Liouville Operator. Journal of Function Spaces and Applications, 2013: 1-7.
• Bas E, Yilmazer R, Panakhov ES, 2013. Fractional Solutions of Bessel Equation with N Method. The Scientific World Journal-Mathematical Analysis, 2013: 1-8.
• Yilmazer R, Bas E, 2012. Fractional Solutions of a Confluent Hypergeometric Equation. Journal of the Chungcheong Mathematical Society, 25 (2): 149-157.
• Sat M, Panakhov ES, 2013. A Uniqueness Theorem for Bessel Operator from Interior Spectral Data. Abstract and Applied Analysis, 2013: 6 pages.
• Sat M, 2014. Half Inverse Problem for the Sturm-Liouville Operator with Coulomb potential. Applied Mathematics and Information Sciences 8(2): 501-504.
• Yilmazer R, Ozturk O, 2013. Explicit Solutions of Singular Differential Equation by means of Fractional Calculus Operators. Abstract and Applied Analysis, 2013: 6 pages.
• Wang PY, Lin SD, Srivastava HM. 2006. Remarks on a Simple Fractional-Calculus Approach to The Solutions of The Bessel Differential Equation of General Order And Some of Its Applications. Comput. Math. Appl. 51: 105-114.
• Lin SD, Ling WC, Nishimoto K, Srivastava HM, 2005. A simple Fractional-Calculus Approach to the Solutions of the Bessel Differential Equation of General Order and Some of its Applications. Comput. Math. Appl. 49: 1487-1498.
• Erde’lyi A, Magnus W, Oberhettinger F, Tricomi FG, 1953. Higher Transcendental Functions. McGraw-Hill Book Company. New York.
• Whittaker ET, Watson GN, 1973. A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; With an Account of the Principal Transcendental Functions. fourth ed. (Reprinted). Cambridge University Press. Cambridge.
• Lin SD, Nishimoto K, 1998. N-Method to a Generalized Associated Legendre equation. J. Fract. Calc. 14: 95-111.
• Lin SD, Nishimoto K, 2000. New Finding of Particular Solutions for a Generalized Associated Legendre Equation. J. Fract. Calc. 18: 9-37.
• Nishimoto K, 2011. Solutions to The Homogeneous Chebyshev’s Equation by Means of N-Fractional Calculus Operator. Research Institute for Mathematical Sciences 1772: 39-63.