Document Zbl 1513.34008

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Appl. Math.</a> <a href="/?q=in%3A489465" title="Articles in this Issue">41, No. 8, Paper No. 398, 31 p. (2022)</a>. </div> <div class="abstract">Summary: Every real-world physical problem is inherently based on uncertainty. It is essential to model the uncertainty then solve, analyze and interpret the result one encounters in the world of vagueness. Generally, science and engineering problems are governed by differential equations. But the parameters, variables and initial conditions involved in the system contain uncertainty due to the lack of information in measurement, observations and experiment. However, It is necessary to develop a comprehensive approach for solving differential equations in an uncertain environment. The purpose of this work is to study and investigate the fuzzy solution of linear third-order fuzzy differential equations using the concept of strongly generalized Hukuhara differentiability (SGHD). To make our analysis possible, we apply the first and second differentiability up to the third-order fuzzy derivative of the fuzzy-valued function. Moreover, we develop an important result concerning the relationship between Laplace transform of fuzzy-valued function and third-order derivative. We construct an algorithm to determine a potential solution of linear third-order fuzzy initial-value problem using the Laplace transform technique. All these solutions are represented in terms of the Mittag-Leffler function involving a single series. Furthermore, we discuss the switching points of linear third-order differential equations and their corresponding solutions in fuzzy environments. To enhance the novelty of the proposed technique, some illustrative examples are presented as applications are analyzed to visualize and support theoretical results.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7645477">Cited in <strong>7</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A34A07" title="MSC2020">34A07</a> </td> <td class="space"> Fuzzy ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34A08" title="MSC2020">34A08</a> </td> <td class="space"> Fractional ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A03E72" title="MSC2020">03E72</a> </td> <td class="space"> Theory of fuzzy sets, etc. </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A33E12" title="MSC2020">33E12</a> </td> <td class="space"> Mittag-Leffler functions and generalizations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34A12" title="MSC2020">34A12</a> </td> <td class="space"> Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34A30" title="MSC2020">34A30</a> </td> <td class="space"> Linear ordinary differential equations and systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A44A10" title="MSC2020">44A10</a> </td> <td class="space"> Laplace transform </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aswitching+points">switching points</a>; <a href="/?q=ut%3Afuzzy+initial-value+problem">fuzzy initial-value problem</a>; <a href="/?q=ut%3Astrongly+generalized+differentiability">strongly generalized differentiability</a>; <a href="/?q=ut%3Afuzzy+Laplace+transform">fuzzy Laplace transform</a>; <a href="/?q=ut%3AMittag-Leffler+function+in+single+series">Mittag-Leffler function in single series</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1513.34008" data-ciurl="/ci/07645477" data-biburl="/bibtex/07645477.bib" data-amsurl="/amsrefs/07645477.bib" data-xmlurl="/xml/07645477.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07645477.pdf" title="Zbl 1513.34008 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/s40314-022-02111-x" aria-label="DOI for “Solution of initial-value problem for linear third-order fuzzy differential equations”" title="10.1007/s40314-022-02111-x">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Ahmadi, MB; 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