A Quantitative Approach to nth-Order Nonlinear Fuzzy Integro-Differential Equation
In recent decades, both the fuzzy differential and fuzzy integral equations have attracted the researcher because the fuzzy operators produce appropriate predictions of problems in an uncertain environment. In this paper, we use fuzzy concepts to study n th -order nonlinear integro-differential equa...
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| Veröffentlicht in: | International journal of applied and computational mathematics 2022, Vol.8 (3) |
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| container_title | International journal of applied and computational mathematics |
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| creator | Ul Haq, Mansoor Ullah, Aman Ahmad, Shabir Akgül, Ali |
| description | In recent decades, both the fuzzy differential and fuzzy integral equations have attracted the researcher because the fuzzy operators produce appropriate predictions of problems in an uncertain environment. In this paper, we use fuzzy concepts to study
n
th
-order nonlinear integro-differential equations. For the proposed problem, through the modified fuzzy Laplace transform method, we derive the general procedure of the solution. To demonstrate the accuracy and appropriateness of the method, we present some numerical problems. We also provide graphical representation by the use of Matlab 2017 to compare the exact and approximate solution. We solve different problems having second-order, fifth-order, and a system of nonlinear fuzzy integro-differential equations through the developed scheme. We simulate the numerical results via 2D and 3D graphs for the different values of uncertainty. In the end, we provide the discussion and concluding remarks of the article. |
| doi_str_mv | 10.1007/s40819-022-01293-6 |
| format | Article |
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n
th
-order nonlinear integro-differential equations. For the proposed problem, through the modified fuzzy Laplace transform method, we derive the general procedure of the solution. To demonstrate the accuracy and appropriateness of the method, we present some numerical problems. We also provide graphical representation by the use of Matlab 2017 to compare the exact and approximate solution. We solve different problems having second-order, fifth-order, and a system of nonlinear fuzzy integro-differential equations through the developed scheme. We simulate the numerical results via 2D and 3D graphs for the different values of uncertainty. In the end, we provide the discussion and concluding remarks of the article.</description><identifier>ISSN: 2349-5103</identifier><identifier>EISSN: 2199-5796</identifier><identifier>DOI: 10.1007/s40819-022-01293-6</identifier><language>eng</language><publisher>New Delhi: Springer India</publisher><subject>Applications of Mathematics ; Applied mathematics ; Computational mathematics ; Computational Science and Engineering ; Differential equations ; Graphical representations ; Integral equations ; Laplace transforms ; Mathematical analysis ; Mathematical and Computational Physics ; Mathematical Modeling and Industrial Mathematics ; Mathematics ; Mathematics and Statistics ; Nuclear Energy ; Operations Research/Decision Theory ; Operators (mathematics) ; Original Paper ; Theoretical</subject><ispartof>International journal of applied and computational mathematics, 2022, Vol.8 (3)</ispartof><rights>The Author(s), under exclusive licence to Springer Nature India Private Limited 2022</rights><rights>The Author(s), under exclusive licence to Springer Nature India Private Limited 2022.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s40819-022-01293-6$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40819-022-01293-6$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Ul Haq, Mansoor</creatorcontrib><creatorcontrib>Ullah, Aman</creatorcontrib><creatorcontrib>Ahmad, Shabir</creatorcontrib><creatorcontrib>Akgül, Ali</creatorcontrib><title>A Quantitative Approach to nth-Order Nonlinear Fuzzy Integro-Differential Equation</title><title>International journal of applied and computational mathematics</title><addtitle>Int. J. Appl. Comput. Math</addtitle><description>In recent decades, both the fuzzy differential and fuzzy integral equations have attracted the researcher because the fuzzy operators produce appropriate predictions of problems in an uncertain environment. In this paper, we use fuzzy concepts to study
n
th
-order nonlinear integro-differential equations. For the proposed problem, through the modified fuzzy Laplace transform method, we derive the general procedure of the solution. To demonstrate the accuracy and appropriateness of the method, we present some numerical problems. We also provide graphical representation by the use of Matlab 2017 to compare the exact and approximate solution. We solve different problems having second-order, fifth-order, and a system of nonlinear fuzzy integro-differential equations through the developed scheme. We simulate the numerical results via 2D and 3D graphs for the different values of uncertainty. In the end, we provide the discussion and concluding remarks of the article.</description><subject>Applications of Mathematics</subject><subject>Applied mathematics</subject><subject>Computational mathematics</subject><subject>Computational Science and Engineering</subject><subject>Differential equations</subject><subject>Graphical representations</subject><subject>Integral equations</subject><subject>Laplace transforms</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Modeling and Industrial Mathematics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Nuclear Energy</subject><subject>Operations Research/Decision Theory</subject><subject>Operators (mathematics)</subject><subject>Original Paper</subject><subject>Theoretical</subject><issn>2349-5103</issn><issn>2199-5796</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNpFkF1LwzAUhoMoOOb-gFcBr6Mnn20ux9x0MByKXoe0TbeOkXZpKrhfb7SCV-e9eM57Dg9CtxTuKUD20AvIqSbAGAHKNCfqAk0Y1ZrITKvLlLlImQK_RrO-PwAAoyIDlk_Q2xy_DtbHJtrYfDo877rQ2nKPY4t93JNtqFzAL60_Nt7ZgFfD-fyF1z66XWjJY1PXLri0bo94eRpSR-tv0FVtj72b_c0p-lgt3xfPZLN9Wi_mG9JRwRShFeNQsVpK6SrJc1aUVa5VlhXasrKkUNRFVavcccutogKksIqBKzMmnBAln6K7sTd9fBpcH82hHYJPJw1TQmmlNZWJ4iPVd6HxOxf-KQrmx58Z_Znkz_z6M4p_A8p-YsY</recordid><startdate>2022</startdate><enddate>2022</enddate><creator>Ul Haq, Mansoor</creator><creator>Ullah, Aman</creator><creator>Ahmad, Shabir</creator><creator>Akgül, Ali</creator><general>Springer India</general><general>Springer Nature B.V</general><scope/></search><sort><creationdate>2022</creationdate><title>A Quantitative Approach to nth-Order Nonlinear Fuzzy Integro-Differential Equation</title><author>Ul Haq, Mansoor ; Ullah, Aman ; Ahmad, Shabir ; Akgül, Ali</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p1426-1d230d2f555ed5382bcd89677b9a2cc10bfbdf68e3a3a614054a620ec724e44c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Applications of Mathematics</topic><topic>Applied mathematics</topic><topic>Computational mathematics</topic><topic>Computational Science and Engineering</topic><topic>Differential equations</topic><topic>Graphical representations</topic><topic>Integral equations</topic><topic>Laplace transforms</topic><topic>Mathematical analysis</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Modeling and Industrial Mathematics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Nuclear Energy</topic><topic>Operations Research/Decision Theory</topic><topic>Operators (mathematics)</topic><topic>Original Paper</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ul Haq, Mansoor</creatorcontrib><creatorcontrib>Ullah, Aman</creatorcontrib><creatorcontrib>Ahmad, Shabir</creatorcontrib><creatorcontrib>Akgül, Ali</creatorcontrib><jtitle>International journal of applied and computational mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ul Haq, Mansoor</au><au>Ullah, Aman</au><au>Ahmad, Shabir</au><au>Akgül, Ali</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Quantitative Approach to nth-Order Nonlinear Fuzzy Integro-Differential Equation</atitle><jtitle>International journal of applied and computational mathematics</jtitle><stitle>Int. J. Appl. Comput. Math</stitle><date>2022</date><risdate>2022</risdate><volume>8</volume><issue>3</issue><issn>2349-5103</issn><eissn>2199-5796</eissn><abstract>In recent decades, both the fuzzy differential and fuzzy integral equations have attracted the researcher because the fuzzy operators produce appropriate predictions of problems in an uncertain environment. In this paper, we use fuzzy concepts to study
n
th
-order nonlinear integro-differential equations. For the proposed problem, through the modified fuzzy Laplace transform method, we derive the general procedure of the solution. To demonstrate the accuracy and appropriateness of the method, we present some numerical problems. We also provide graphical representation by the use of Matlab 2017 to compare the exact and approximate solution. We solve different problems having second-order, fifth-order, and a system of nonlinear fuzzy integro-differential equations through the developed scheme. We simulate the numerical results via 2D and 3D graphs for the different values of uncertainty. In the end, we provide the discussion and concluding remarks of the article.</abstract><cop>New Delhi</cop><pub>Springer India</pub><doi>10.1007/s40819-022-01293-6</doi></addata></record> |
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| source | SpringerNature Complete Journals |
| subjects | Applications of Mathematics Applied mathematics Computational mathematics Computational Science and Engineering Differential equations Graphical representations Integral equations Laplace transforms Mathematical analysis Mathematical and Computational Physics Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Nuclear Energy Operations Research/Decision Theory Operators (mathematics) Original Paper Theoretical |
| title | A Quantitative Approach to nth-Order Nonlinear Fuzzy Integro-Differential Equation |
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