Abstract
Fractional calculus theory includes defnition of the derivatives and integrals of arbitrary order. This
theory is used to solve some classes of singular differential equations and fractional order differential equations.
One of these equations is the confluent hypergeometric equation. In this paper, we intend to solve this equation by
applying
1
1 A Different Solution Method for the Confluent Hypergeometric Equation
2
3 ABSTRACT: Fractional calculus theory includes definition of the derivatives and
4 integrals of arbitrary order. This theory is used to solve some classes of singular
5 differential equations and fractional order differential equations. One of these equations
6 is the confluent hypergeometric equation. In this paper, we intend to solve this equation
7 by applying
References
- Akgül A, 2014. A new method for approximate solutions of fractional order boundary value problems. Neural Parallel and Scientific Computations 22(1-2): 223-237.
- Akgül A, Inc M, Karatas E, Baleanu D, 2015. Numerical solutions of fractional differential equations of Lane-Emden type by an accurate technique. Advances in Difference Equations, 220: 12 pages.
- Akgül A, Kılıçman A, Inc M, 2013. Improved (G′/G)-expansion method for the space and time fractional foam drainage and KdV equations. Abstract and Applied Analysis, 2013: 7 pages.
- Bayın S, 2006. Mathematical Methods in Science and Engineering. John Wiley & Sons, USA, 709p.
- 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. Computers & Mathematics with Applications, 49: 1487-1498.
- Miller K, Ross B, 1993. An Introduction to the Fractional Calculus and Fractional Differential Equations. John Wiley & Sons, USA, 376p.
- Oldham K, Spanier J, 1974. The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order. Academic Press, USA, 240p.
- 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, 365p.
- 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. Computers & Mathematics with Applications, 51: 105-114.
- Yilmazer R, Ozturk O, 2013. Explicit Solutions of Singular Differential Equation by means of Fractional Calculus Operators. Abstract and Applied Analysis, 2013: 6 pages.
Abstract
Kesirli hesap teorisi, keyf mertebeden türev ve integral tanımını kapsamaktadır. Diferansiyel denklemlerin ve kesirli diferansiyel denklemlerin bazı sınıflarını çözmek için bu teori kullanılmaktadır. Bu denklemlerden birisi
konfluent hipergeometrik denklemidir. Bu makalede, farklı bir çözüm metodu olarak metodunun uygulanmasıyla bu denklemi çözmeyi hedeflemekteyiz.
Keywords
References
- Akgül A, 2014. A new method for approximate solutions of fractional order boundary value problems. Neural Parallel and Scientific Computations 22(1-2): 223-237.
- Akgül A, Inc M, Karatas E, Baleanu D, 2015. Numerical solutions of fractional differential equations of Lane-Emden type by an accurate technique. Advances in Difference Equations, 220: 12 pages.
- Akgül A, Kılıçman A, Inc M, 2013. Improved (G′/G)-expansion method for the space and time fractional foam drainage and KdV equations. Abstract and Applied Analysis, 2013: 7 pages.
- Bayın S, 2006. Mathematical Methods in Science and Engineering. John Wiley & Sons, USA, 709p.
- 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. Computers & Mathematics with Applications, 49: 1487-1498.
- Miller K, Ross B, 1993. An Introduction to the Fractional Calculus and Fractional Differential Equations. John Wiley & Sons, USA, 376p.
- Oldham K, Spanier J, 1974. The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order. Academic Press, USA, 240p.
- 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, 365p.
- 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. Computers & Mathematics with Applications, 51: 105-114.
- Yilmazer R, Ozturk O, 2013. Explicit Solutions of Singular Differential Equation by means of Fractional Calculus Operators. Abstract and Applied Analysis, 2013: 6 pages.
Details
| Primary Language | English |
|---|---|
| Journal Section | Matematik / Mathematics |
| Authors | |
| Publication Date | June 30, 2017 |
| Submission Date | July 28, 2016 |
| Acceptance Date | October 6, 2016 |
| Published in Issue | Year 2017 Volume: 7 Issue: 2 |