Solving Fractional Nonlinear Fredholm Integro-differential Equations via Hybrid of Rationalized Haar Functions

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Volume 9, Issue 3

Yadollah Ordokhani and Neda Rahimi

J. Info. Comput. Sci. , 9 (2014), pp. 169-180.

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Abstract

This paper presents hybrid of rationalized Haar (HRH) functions method for approximate the numerical solution of the fractional nonlinear Fredholm integro-differential equations (FNFIDEs). The fractional derivatives are considered in the sense of Caputo. The fractional operational matrix of hybrid of block-pulse and rationalized Haar functions are presented. This matrix together with the dual operational matrix are used to reduce the computation of FNFIDEs into a system of algebraic equations. Some numerical examples are given and the results of applying this method demonstrate time and computational are small.

Keywords

Fredholm integro-differential equation, Riemann-Liouville integral, Caputo fractional derivative, Fractional operational matrix, Rationalized Haar, Hybrid.

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@Article{JICS-9-169, author = {Yadollah Ordokhani and Neda Rahimi}, title = {Solving Fractional Nonlinear Fredholm Integro-differential Equations via Hybrid of Rationalized Haar Functions}, journal = {Journal of Information and Computing Science}, year = {2014}, volume = {9}, number = {3}, pages = {169--180}, abstract = { This paper presents hybrid of rationalized Haar (HRH) functions method for approximate the numerical solution of the fractional nonlinear Fredholm integro-differential equations (FNFIDEs). The fractional derivatives are considered in the sense of Caputo. The fractional operational matrix of hybrid of block-pulse and rationalized Haar functions are presented. This matrix together with the dual operational matrix are used to reduce the computation of FNFIDEs into a system of algebraic equations. Some numerical examples are given and the results of applying this method demonstrate time and computational are small. }, issn = {3080-180X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jics/22577.html} }

TY - JOUR T1 - Solving Fractional Nonlinear Fredholm Integro-differential Equations via Hybrid of Rationalized Haar Functions AU - Yadollah Ordokhani and Neda Rahimi JO - Journal of Information and Computing Science VL - 3 SP - 169 EP - 180 PY - 2014 DA - 2014/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jics/22577.html KW - Fredholm integro-differential equation, Riemann-Liouville integral, Caputo fractional derivative, Fractional operational matrix, Rationalized Haar, Hybrid. AB - This paper presents hybrid of rationalized Haar (HRH) functions method for approximate the numerical solution of the fractional nonlinear Fredholm integro-differential equations (FNFIDEs). The fractional derivatives are considered in the sense of Caputo. The fractional operational matrix of hybrid of block-pulse and rationalized Haar functions are presented. This matrix together with the dual operational matrix are used to reduce the computation of FNFIDEs into a system of algebraic equations. Some numerical examples are given and the results of applying this method demonstrate time and computational are small.

Yadollah Ordokhani and Neda Rahimi. (2014). Solving Fractional Nonlinear Fredholm Integro-differential Equations via Hybrid of Rationalized Haar Functions. Journal of Information and Computing Science. 9 (3). 169-180. doi:

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