Loading…
A new iterative method with ρ-Laplace transform for solving fractional differential equations with Caputo generalized fractional derivative
In this paper, the new iterative method with ρ -Laplace transform of getting the approximate solution of fractional differential equations was proposed with Caputo generalized fractional derivative. The effect of the various value of order α and parameter ρ in the solution of certain well known frac...
Saved in:
| Published in: | Engineering with computers 2022-06, Vol.38 (3), p.2125-2138 |
|---|---|
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| cited_by | cdi_FETCH-LOGICAL-c319t-76262b8ef26d0b31ba938385933807fbac7546889707def0c9385dd326cc5d393 |
|---|---|
| cites | cdi_FETCH-LOGICAL-c319t-76262b8ef26d0b31ba938385933807fbac7546889707def0c9385dd326cc5d393 |
| container_end_page | 2138 |
| container_issue | 3 |
| container_start_page | 2125 |
| container_title | Engineering with computers |
| container_volume | 38 |
| creator | Bhangale, Nikita Kachhia, Krunal B. Gómez-Aguilar, J. F. |
| description | In this paper, the new iterative method with
ρ
-Laplace transform of getting the approximate solution of fractional differential equations was proposed with Caputo generalized fractional derivative. The effect of the various value of order
α
and parameter
ρ
in the solution of certain well known fractional differential equation with Caputo generalized fractional derivative. Applications to the certain fractional differential equation in various systems demonstrate that the proposed method is more reliable and powerful. The graphical representations of the approximate analytic solutions of the fractional differential equations described by the Caputo generalized fractional derivative were provided and the nature of the achieved solution in terms of plots for distinct arbitrary order is captured. |
| doi_str_mv | 10.1007/s00366-020-01202-9 |
| format | article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2672837805</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2672837805</sourcerecordid><originalsourceid>FETCH-LOGICAL-c319t-76262b8ef26d0b31ba938385933807fbac7546889707def0c9385dd326cc5d393</originalsourceid><addsrcrecordid>eNp9UM1KAzEQDqJgrb6Ap4Dn6CTpJrvHUvyDghc9h3R30qZsd9skrejNu-_mK7ntCuLFywwz8_0MHyGXHK45gL6JAFIpBgIYcAGCFUdkwEcyY5lS8pgMgGvNQCl9Ss5iXAJwCVAMyOeYNvhKfcJgk98hXWFatBV99WlBvz7Y1K5rWyJNwTbRtWFFu0JjW-98M6cu2DL5trE1rbxzGLBJvhtws7X7fex1Jna9TS2dY9O51P4dqz9MDH53MD8nJ87WES9--pC83N0-Tx7Y9On-cTKeslLyIjGthBKzHJ1QFcwkn9lC5jLPCilz0G5mS52NVJ4XGnSFDsrunFWVFKoss0oWckiuet11aDdbjMks223ofolGKC1yqXPIOpToUWVoYwzozDr4lQ1vhoPZp2761E2XujmkbvbSsifFDtzMMfxK_8P6Bt5EiD8</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2672837805</pqid></control><display><type>article</type><title>A new iterative method with ρ-Laplace transform for solving fractional differential equations with Caputo generalized fractional derivative</title><source>Springer Link</source><creator>Bhangale, Nikita ; Kachhia, Krunal B. ; Gómez-Aguilar, J. F.</creator><creatorcontrib>Bhangale, Nikita ; Kachhia, Krunal B. ; Gómez-Aguilar, J. F.</creatorcontrib><description>In this paper, the new iterative method with
ρ
-Laplace transform of getting the approximate solution of fractional differential equations was proposed with Caputo generalized fractional derivative. The effect of the various value of order
α
and parameter
ρ
in the solution of certain well known fractional differential equation with Caputo generalized fractional derivative. Applications to the certain fractional differential equation in various systems demonstrate that the proposed method is more reliable and powerful. The graphical representations of the approximate analytic solutions of the fractional differential equations described by the Caputo generalized fractional derivative were provided and the nature of the achieved solution in terms of plots for distinct arbitrary order is captured.</description><identifier>ISSN: 0177-0667</identifier><identifier>EISSN: 1435-5663</identifier><identifier>DOI: 10.1007/s00366-020-01202-9</identifier><language>eng</language><publisher>London: Springer London</publisher><subject>CAE) and Design ; Calculus ; Calculus of Variations and Optimal Control; Optimization ; Classical Mechanics ; Computer Science ; Computer-Aided Engineering (CAD ; Control ; Differential equations ; Engineering ; Exact solutions ; Fractional calculus ; Graphical representations ; Iterative methods ; Laplace transforms ; Math. Applications in Chemistry ; Mathematical analysis ; Mathematical and Computational Engineering ; Original Article ; Partial differential equations ; Physics ; Systems Theory</subject><ispartof>Engineering with computers, 2022-06, Vol.38 (3), p.2125-2138</ispartof><rights>Springer-Verlag London Ltd., part of Springer Nature 2020</rights><rights>Springer-Verlag London Ltd., part of Springer Nature 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-76262b8ef26d0b31ba938385933807fbac7546889707def0c9385dd326cc5d393</citedby><cites>FETCH-LOGICAL-c319t-76262b8ef26d0b31ba938385933807fbac7546889707def0c9385dd326cc5d393</cites><orcidid>0000-0001-9403-3767</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Bhangale, Nikita</creatorcontrib><creatorcontrib>Kachhia, Krunal B.</creatorcontrib><creatorcontrib>Gómez-Aguilar, J. F.</creatorcontrib><title>A new iterative method with ρ-Laplace transform for solving fractional differential equations with Caputo generalized fractional derivative</title><title>Engineering with computers</title><addtitle>Engineering with Computers</addtitle><description>In this paper, the new iterative method with
ρ
-Laplace transform of getting the approximate solution of fractional differential equations was proposed with Caputo generalized fractional derivative. The effect of the various value of order
α
and parameter
ρ
in the solution of certain well known fractional differential equation with Caputo generalized fractional derivative. Applications to the certain fractional differential equation in various systems demonstrate that the proposed method is more reliable and powerful. The graphical representations of the approximate analytic solutions of the fractional differential equations described by the Caputo generalized fractional derivative were provided and the nature of the achieved solution in terms of plots for distinct arbitrary order is captured.</description><subject>CAE) and Design</subject><subject>Calculus</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Classical Mechanics</subject><subject>Computer Science</subject><subject>Computer-Aided Engineering (CAD</subject><subject>Control</subject><subject>Differential equations</subject><subject>Engineering</subject><subject>Exact solutions</subject><subject>Fractional calculus</subject><subject>Graphical representations</subject><subject>Iterative methods</subject><subject>Laplace transforms</subject><subject>Math. Applications in Chemistry</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Engineering</subject><subject>Original Article</subject><subject>Partial differential equations</subject><subject>Physics</subject><subject>Systems Theory</subject><issn>0177-0667</issn><issn>1435-5663</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9UM1KAzEQDqJgrb6Ap4Dn6CTpJrvHUvyDghc9h3R30qZsd9skrejNu-_mK7ntCuLFywwz8_0MHyGXHK45gL6JAFIpBgIYcAGCFUdkwEcyY5lS8pgMgGvNQCl9Ss5iXAJwCVAMyOeYNvhKfcJgk98hXWFatBV99WlBvz7Y1K5rWyJNwTbRtWFFu0JjW-98M6cu2DL5trE1rbxzGLBJvhtws7X7fex1Jna9TS2dY9O51P4dqz9MDH53MD8nJ87WES9--pC83N0-Tx7Y9On-cTKeslLyIjGthBKzHJ1QFcwkn9lC5jLPCilz0G5mS52NVJ4XGnSFDsrunFWVFKoss0oWckiuet11aDdbjMks223ofolGKC1yqXPIOpToUWVoYwzozDr4lQ1vhoPZp2761E2XujmkbvbSsifFDtzMMfxK_8P6Bt5EiD8</recordid><startdate>20220601</startdate><enddate>20220601</enddate><creator>Bhangale, Nikita</creator><creator>Kachhia, Krunal B.</creator><creator>Gómez-Aguilar, J. F.</creator><general>Springer London</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7XB</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0N</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope><orcidid>https://orcid.org/0000-0001-9403-3767</orcidid></search><sort><creationdate>20220601</creationdate><title>A new iterative method with ρ-Laplace transform for solving fractional differential equations with Caputo generalized fractional derivative</title><author>Bhangale, Nikita ; Kachhia, Krunal B. ; Gómez-Aguilar, J. F.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-76262b8ef26d0b31ba938385933807fbac7546889707def0c9385dd326cc5d393</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>CAE) and Design</topic><topic>Calculus</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Classical Mechanics</topic><topic>Computer Science</topic><topic>Computer-Aided Engineering (CAD</topic><topic>Control</topic><topic>Differential equations</topic><topic>Engineering</topic><topic>Exact solutions</topic><topic>Fractional calculus</topic><topic>Graphical representations</topic><topic>Iterative methods</topic><topic>Laplace transforms</topic><topic>Math. Applications in Chemistry</topic><topic>Mathematical analysis</topic><topic>Mathematical and Computational Engineering</topic><topic>Original Article</topic><topic>Partial differential equations</topic><topic>Physics</topic><topic>Systems Theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bhangale, Nikita</creatorcontrib><creatorcontrib>Kachhia, Krunal B.</creatorcontrib><creatorcontrib>Gómez-Aguilar, J. F.</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>AUTh Library subscriptions: ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer science database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Computing Database</collection><collection>Engineering Database</collection><collection>ProQuest advanced technologies & aerospace journals</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering collection</collection><collection>ProQuest Central Basic</collection><jtitle>Engineering with computers</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bhangale, Nikita</au><au>Kachhia, Krunal B.</au><au>Gómez-Aguilar, J. F.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A new iterative method with ρ-Laplace transform for solving fractional differential equations with Caputo generalized fractional derivative</atitle><jtitle>Engineering with computers</jtitle><stitle>Engineering with Computers</stitle><date>2022-06-01</date><risdate>2022</risdate><volume>38</volume><issue>3</issue><spage>2125</spage><epage>2138</epage><pages>2125-2138</pages><issn>0177-0667</issn><eissn>1435-5663</eissn><abstract>In this paper, the new iterative method with
ρ
-Laplace transform of getting the approximate solution of fractional differential equations was proposed with Caputo generalized fractional derivative. The effect of the various value of order
α
and parameter
ρ
in the solution of certain well known fractional differential equation with Caputo generalized fractional derivative. Applications to the certain fractional differential equation in various systems demonstrate that the proposed method is more reliable and powerful. The graphical representations of the approximate analytic solutions of the fractional differential equations described by the Caputo generalized fractional derivative were provided and the nature of the achieved solution in terms of plots for distinct arbitrary order is captured.</abstract><cop>London</cop><pub>Springer London</pub><doi>10.1007/s00366-020-01202-9</doi><tpages>14</tpages><orcidid>https://orcid.org/0000-0001-9403-3767</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0177-0667 |
| ispartof | Engineering with computers, 2022-06, Vol.38 (3), p.2125-2138 |
| issn | 0177-0667 1435-5663 |
| language | eng |
| recordid | cdi_proquest_journals_2672837805 |
| source | Springer Link |
| subjects | CAE) and Design Calculus Calculus of Variations and Optimal Control Optimization Classical Mechanics Computer Science Computer-Aided Engineering (CAD Control Differential equations Engineering Exact solutions Fractional calculus Graphical representations Iterative methods Laplace transforms Math. Applications in Chemistry Mathematical analysis Mathematical and Computational Engineering Original Article Partial differential equations Physics Systems Theory |
| title | A new iterative method with ρ-Laplace transform for solving fractional differential equations with Caputo generalized fractional derivative |
| url | http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-29T11%3A27%3A26IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20new%20iterative%20method%20with%20%CF%81-Laplace%20transform%20for%20solving%20fractional%20differential%20equations%20with%20Caputo%20generalized%20fractional%20derivative&rft.jtitle=Engineering%20with%20computers&rft.au=Bhangale,%20Nikita&rft.date=2022-06-01&rft.volume=38&rft.issue=3&rft.spage=2125&rft.epage=2138&rft.pages=2125-2138&rft.issn=0177-0667&rft.eissn=1435-5663&rft_id=info:doi/10.1007/s00366-020-01202-9&rft_dat=%3Cproquest_cross%3E2672837805%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c319t-76262b8ef26d0b31ba938385933807fbac7546889707def0c9385dd326cc5d393%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2672837805&rft_id=info:pmid/&rfr_iscdi=true |