A local meshless radial basis functions based method for solving fractional integral equations
This paper presents a Localized Radial Basis Functions Collocation Method (LRBFCM) for numerically solving one and 2-dimensional Fractional Integral Equations (2D-FIEs). The LRBFCM approach decomposes the main problem into several local sub-problems of small sizes, effectively reducing the ill-condi...
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REA Press
2023-03-01
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| Series: | Computational Algorithms and Numerical Dimensions |
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| Online Access: | https://www.journal-cand.com/article_188639_91ace27fdc12908d7096894ec8e3b838.pdf |
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| author | Mehdi Radmanesh Mohammad Ebadi |
| author_facet | Mehdi Radmanesh Mohammad Ebadi |
| author_sort | Mehdi Radmanesh |
| collection | DOAJ |
| description | This paper presents a Localized Radial Basis Functions Collocation Method (LRBFCM) for numerically solving one and 2-dimensional Fractional Integral Equations (2D-FIEs). The LRBFCM approach decomposes the main problem into several local sub-problems of small sizes, effectively reducing the ill-conditioning of the overall problem. By employing the collocation approach and utilizing the strong form of the equation, the proposed method achieves efficiency. Additionally, the matrix operations only require the inversion of small-sized matrices, further contributing to the method's efficiency. To demonstrate the effectiveness of the LRBFCM, the paper provides test problems encompassing linear, nonlinear, Volterra, and Fredholm types of Fractional Integral Equations (FIEs). The numerical results showcase the efficiency of the proposed method, validating its performance in solving various types of FIEs. |
| format | Article |
| id | doaj-art-b8a0ee3720564ab2ae9fba878b828a05 |
| institution | Kabale University |
| issn | 2980-7646 2980-9320 |
| language | English |
| publishDate | 2023-03-01 |
| publisher | REA Press |
| record_format | Article |
| series | Computational Algorithms and Numerical Dimensions |
| spelling | doaj-art-b8a0ee3720564ab2ae9fba878b828a052025-01-30T11:21:28ZengREA PressComputational Algorithms and Numerical Dimensions2980-76462980-93202023-03-0121354610.22105/cand.2023.400616.1064188639A local meshless radial basis functions based method for solving fractional integral equationsMehdi Radmanesh0Mohammad Ebadi1Department of Mathematics, Graduate University of Advanced Technology of Kerman, Kerman, Iran.Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy.This paper presents a Localized Radial Basis Functions Collocation Method (LRBFCM) for numerically solving one and 2-dimensional Fractional Integral Equations (2D-FIEs). The LRBFCM approach decomposes the main problem into several local sub-problems of small sizes, effectively reducing the ill-conditioning of the overall problem. By employing the collocation approach and utilizing the strong form of the equation, the proposed method achieves efficiency. Additionally, the matrix operations only require the inversion of small-sized matrices, further contributing to the method's efficiency. To demonstrate the effectiveness of the LRBFCM, the paper provides test problems encompassing linear, nonlinear, Volterra, and Fredholm types of Fractional Integral Equations (FIEs). The numerical results showcase the efficiency of the proposed method, validating its performance in solving various types of FIEs.https://www.journal-cand.com/article_188639_91ace27fdc12908d7096894ec8e3b838.pdffractional calculuslocal meshless methodsfractional integral equationscollocation methods |
| spellingShingle | Mehdi Radmanesh Mohammad Ebadi A local meshless radial basis functions based method for solving fractional integral equations Computational Algorithms and Numerical Dimensions fractional calculus local meshless methods fractional integral equations collocation methods |
| title | A local meshless radial basis functions based method for solving fractional integral equations |
| title_full | A local meshless radial basis functions based method for solving fractional integral equations |
| title_fullStr | A local meshless radial basis functions based method for solving fractional integral equations |
| title_full_unstemmed | A local meshless radial basis functions based method for solving fractional integral equations |
| title_short | A local meshless radial basis functions based method for solving fractional integral equations |
| title_sort | local meshless radial basis functions based method for solving fractional integral equations |
| topic | fractional calculus local meshless methods fractional integral equations collocation methods |
| url | https://www.journal-cand.com/article_188639_91ace27fdc12908d7096894ec8e3b838.pdf |
| work_keys_str_mv | AT mehdiradmanesh alocalmeshlessradialbasisfunctionsbasedmethodforsolvingfractionalintegralequations AT mohammadebadi alocalmeshlessradialbasisfunctionsbasedmethodforsolvingfractionalintegralequations AT mehdiradmanesh localmeshlessradialbasisfunctionsbasedmethodforsolvingfractionalintegralequations AT mohammadebadi localmeshlessradialbasisfunctionsbasedmethodforsolvingfractionalintegralequations |