A novel numerical scheme for fractional differential equations using extreme learning machine

In this paper, we propose a neural network-based approach with an Extreme Learning Machine (ELM) for solving fractional differential equations. The solution procedure for the linear and nonlinear fractional differential equations has been derived. Also the convergence and stability of the proposed m...
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Gespeichert in:

Autor*in:	S M, Sivalingam [verfasserIn] Kumar, Pushpendra [verfasserIn] Govindaraj, V. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Extreme learning machine Neural networks Legendre polynomials Operational matrix

Übergeordnetes Werk:	Enthalten in: Physica / A - Amsterdam : North Holland Publ. Co., 1975, 622
Übergeordnetes Werk:	volume:622

DOI / URN:	10.1016/j.physa.2023.128887

Katalog-ID:	ELV010138242

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245	1	0	\|a A novel numerical scheme for fractional differential equations using extreme learning machine
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allfields	10.1016/j.physa.2023.128887 doi (DE-627)ELV010138242 (ELSEVIER)S0378-4371(23)00442-9 DE-627 ger DE-627 rda eng 500 VZ 33.25 bkl 31.00 bkl S M, Sivalingam verfasserin (orcid)0000-0003-0818-9007 aut A novel numerical scheme for fractional differential equations using extreme learning machine 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we propose a neural network-based approach with an Extreme Learning Machine (ELM) for solving fractional differential equations. The solution procedure for the linear and nonlinear fractional differential equations has been derived. Also the convergence and stability of the proposed method is provided. Then we examine the numerical solution of several fractional-order ordinary and partial differential equations. As a last example the Burgers equation without an explicit exact solution. The effect of changing the number of neurons on the accuracy of the solution is obtained graphically. Extreme learning machine Neural networks Legendre polynomials Operational matrix Kumar, Pushpendra verfasserin aut Govindaraj, V. verfasserin aut Enthalten in Physica / A Amsterdam : North Holland Publ. Co., 1975 622 Online-Ressource (DE-627)266015077 (DE-600)1466577-3 (DE-576)074959832 1873-2119 nnns volume:622 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 33.25 Thermodynamik statistische Physik VZ 31.00 Mathematik: Allgemeines VZ AR 622
spelling	10.1016/j.physa.2023.128887 doi (DE-627)ELV010138242 (ELSEVIER)S0378-4371(23)00442-9 DE-627 ger DE-627 rda eng 500 VZ 33.25 bkl 31.00 bkl S M, Sivalingam verfasserin (orcid)0000-0003-0818-9007 aut A novel numerical scheme for fractional differential equations using extreme learning machine 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we propose a neural network-based approach with an Extreme Learning Machine (ELM) for solving fractional differential equations. The solution procedure for the linear and nonlinear fractional differential equations has been derived. Also the convergence and stability of the proposed method is provided. Then we examine the numerical solution of several fractional-order ordinary and partial differential equations. As a last example the Burgers equation without an explicit exact solution. The effect of changing the number of neurons on the accuracy of the solution is obtained graphically. Extreme learning machine Neural networks Legendre polynomials Operational matrix Kumar, Pushpendra verfasserin aut Govindaraj, V. verfasserin aut Enthalten in Physica / A Amsterdam : North Holland Publ. Co., 1975 622 Online-Ressource (DE-627)266015077 (DE-600)1466577-3 (DE-576)074959832 1873-2119 nnns volume:622 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 33.25 Thermodynamik statistische Physik VZ 31.00 Mathematik: Allgemeines VZ AR 622
allfields_unstemmed	10.1016/j.physa.2023.128887 doi (DE-627)ELV010138242 (ELSEVIER)S0378-4371(23)00442-9 DE-627 ger DE-627 rda eng 500 VZ 33.25 bkl 31.00 bkl S M, Sivalingam verfasserin (orcid)0000-0003-0818-9007 aut A novel numerical scheme for fractional differential equations using extreme learning machine 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we propose a neural network-based approach with an Extreme Learning Machine (ELM) for solving fractional differential equations. The solution procedure for the linear and nonlinear fractional differential equations has been derived. Also the convergence and stability of the proposed method is provided. Then we examine the numerical solution of several fractional-order ordinary and partial differential equations. As a last example the Burgers equation without an explicit exact solution. The effect of changing the number of neurons on the accuracy of the solution is obtained graphically. Extreme learning machine Neural networks Legendre polynomials Operational matrix Kumar, Pushpendra verfasserin aut Govindaraj, V. verfasserin aut Enthalten in Physica / A Amsterdam : North Holland Publ. Co., 1975 622 Online-Ressource (DE-627)266015077 (DE-600)1466577-3 (DE-576)074959832 1873-2119 nnns volume:622 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 33.25 Thermodynamik statistische Physik VZ 31.00 Mathematik: Allgemeines VZ AR 622
allfieldsGer	10.1016/j.physa.2023.128887 doi (DE-627)ELV010138242 (ELSEVIER)S0378-4371(23)00442-9 DE-627 ger DE-627 rda eng 500 VZ 33.25 bkl 31.00 bkl S M, Sivalingam verfasserin (orcid)0000-0003-0818-9007 aut A novel numerical scheme for fractional differential equations using extreme learning machine 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we propose a neural network-based approach with an Extreme Learning Machine (ELM) for solving fractional differential equations. The solution procedure for the linear and nonlinear fractional differential equations has been derived. Also the convergence and stability of the proposed method is provided. Then we examine the numerical solution of several fractional-order ordinary and partial differential equations. As a last example the Burgers equation without an explicit exact solution. The effect of changing the number of neurons on the accuracy of the solution is obtained graphically. Extreme learning machine Neural networks Legendre polynomials Operational matrix Kumar, Pushpendra verfasserin aut Govindaraj, V. verfasserin aut Enthalten in Physica / A Amsterdam : North Holland Publ. Co., 1975 622 Online-Ressource (DE-627)266015077 (DE-600)1466577-3 (DE-576)074959832 1873-2119 nnns volume:622 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 33.25 Thermodynamik statistische Physik VZ 31.00 Mathematik: Allgemeines VZ AR 622
allfieldsSound	10.1016/j.physa.2023.128887 doi (DE-627)ELV010138242 (ELSEVIER)S0378-4371(23)00442-9 DE-627 ger DE-627 rda eng 500 VZ 33.25 bkl 31.00 bkl S M, Sivalingam verfasserin (orcid)0000-0003-0818-9007 aut A novel numerical scheme for fractional differential equations using extreme learning machine 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we propose a neural network-based approach with an Extreme Learning Machine (ELM) for solving fractional differential equations. The solution procedure for the linear and nonlinear fractional differential equations has been derived. Also the convergence and stability of the proposed method is provided. Then we examine the numerical solution of several fractional-order ordinary and partial differential equations. As a last example the Burgers equation without an explicit exact solution. The effect of changing the number of neurons on the accuracy of the solution is obtained graphically. Extreme learning machine Neural networks Legendre polynomials Operational matrix Kumar, Pushpendra verfasserin aut Govindaraj, V. verfasserin aut Enthalten in Physica / A Amsterdam : North Holland Publ. Co., 1975 622 Online-Ressource (DE-627)266015077 (DE-600)1466577-3 (DE-576)074959832 1873-2119 nnns volume:622 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 33.25 Thermodynamik statistische Physik VZ 31.00 Mathematik: Allgemeines VZ AR 622
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author	S M, Sivalingam
spellingShingle	S M, Sivalingam ddc 500 bkl 33.25 bkl 31.00 misc Extreme learning machine misc Neural networks misc Legendre polynomials misc Operational matrix A novel numerical scheme for fractional differential equations using extreme learning machine
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title	A novel numerical scheme for fractional differential equations using extreme learning machine
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title_full	A novel numerical scheme for fractional differential equations using extreme learning machine
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author_browse	S M, Sivalingam Kumar, Pushpendra Govindaraj, V.
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title_sort	a novel numerical scheme for fractional differential equations using extreme learning machine
title_auth	A novel numerical scheme for fractional differential equations using extreme learning machine
abstract	In this paper, we propose a neural network-based approach with an Extreme Learning Machine (ELM) for solving fractional differential equations. The solution procedure for the linear and nonlinear fractional differential equations has been derived. Also the convergence and stability of the proposed method is provided. Then we examine the numerical solution of several fractional-order ordinary and partial differential equations. As a last example the Burgers equation without an explicit exact solution. The effect of changing the number of neurons on the accuracy of the solution is obtained graphically.
abstractGer	In this paper, we propose a neural network-based approach with an Extreme Learning Machine (ELM) for solving fractional differential equations. The solution procedure for the linear and nonlinear fractional differential equations has been derived. Also the convergence and stability of the proposed method is provided. Then we examine the numerical solution of several fractional-order ordinary and partial differential equations. As a last example the Burgers equation without an explicit exact solution. The effect of changing the number of neurons on the accuracy of the solution is obtained graphically.
abstract_unstemmed	In this paper, we propose a neural network-based approach with an Extreme Learning Machine (ELM) for solving fractional differential equations. The solution procedure for the linear and nonlinear fractional differential equations has been derived. Also the convergence and stability of the proposed method is provided. Then we examine the numerical solution of several fractional-order ordinary and partial differential equations. As a last example the Burgers equation without an explicit exact solution. The effect of changing the number of neurons on the accuracy of the solution is obtained graphically.
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title_short	A novel numerical scheme for fractional differential equations using extreme learning machine
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doi_str	10.1016/j.physa.2023.128887
up_date	2024-07-06T16:57:16.340Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">ELV010138242</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230927093420.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">230604s2023 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1016/j.physa.2023.128887</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)ELV010138242</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ELSEVIER)S0378-4371(23)00442-9</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">500</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">33.25</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.00</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">S M, Sivalingam</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0003-0818-9007</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">A novel numerical scheme for fractional differential equations using extreme learning machine</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2023</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zzz</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">In this paper, we propose a neural network-based approach with an Extreme Learning Machine (ELM) for solving fractional differential equations. 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A novel numerical scheme for fractional differential equations using extreme learning machine

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