Sains Malaysiana 48(1)(2019): 251–257

http://dx.doi.org/10.17576/jsm-2019-4801-29

 

Solving Fractional Fredholm Integro-Differential Equations by Laguerre Polynomials

(Penyelesaian Pecahan Persamaan Pembezaan-Kamiran Fredholm menggunakan Polinomial Laguerre)

 

AYŞEGÜL DAŞCIOĞLU & DİLEK VAROL BAYRAM*

 

Department of Mathematics, Faculty of Science and Arts, Pamukkale University, Denizli, 20070, Turkey

 

Received: 16 February 2018/Accepted: 13 September 2018

 

ABSTRACT

The main purpose of this study was to present an approximation method based on the Laguerre polynomials to obtain the solutions of the fractional linear Fredholm integro-differential equations. This method transforms the integro-differential equation to a system of linear algebraic equations by using the collocation points. In addition, the matrix relation for Caputo fractional derivative of Laguerre polynomials is also obtained. Besides, some examples are presented to illustrate the accuracy of the method and the results are discussed.

 

Keywords: Fractional integro-differential equations; Fredholm integro-differential equations; Laguerre polynomials

 

ABSTRAK

Tujuan utama kajian ini adalah untuk mengemukakan kaedah penghampiran berdasarkan polinomial Laguerre untuk mendapatkan penyelesaian pecahan linear persamaan pembezaan-kamiran Fredholm. Kaedah ini menjelmakan persamaan pembezaan-kamiran ke sistem persamaan aljabar linear dengan menggunakan titik-titik kolokasi. Di samping itu, hubungan matriks untuk terbitan pecahan Caputo polinomial Laguerre juga diperoleh. Selain itu, beberapa contoh dibentangkan untuk menggambarkan ketepatan kaedah dan hasilnya dibincangkan.

 

Kata kunci: Persamaan pembezaan-kamiran Fredholm; persamaan pembezaan-kamiran pecahan; polinomial Laguerre

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*Corresponding author; email: dvarol@pau.edu.tr