Document Zbl 1542.34002

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Sci.</a> <a href="/?q=in%3A511701" title="Articles in this Issue">645, Article ID 119372, 27 p. (2023)</a>. </div> <div class="abstract">Summary: Fuzzy fractional models have attracted considerable attention because of their comprehensive and broader understanding of real-world problems. Analytical studies of these models are often complex and difficult. Therefore, it is beneficial to develop a suitable and comprehensive technique to solve these models analytically. In this paper, an explicit analytical technique for solving two-dimensional incommensurate linear fuzzy systems of fractional Caputo differential equations (FLSoCFDEs) considering generalized Hukuhara differentiability ($gH$-differentiability) is presented and demonstrated. This extracted explicit solution is presented for different classes of such systems, including homogeneous and non-homogeneous cases with commensurate and incommensurate fractional orders. Moreover, the potential solution of FLSoCFDEs in terms of the Mittag-Leffler function involving double series is presented. The originality of the proposed technique is that the fuzzy Cauchy problem is transformed into a system of fuzzy linear Volterra integral equations of second kind and then the solution is extracted using the iterative Picard scheme based on the Banach fixed point theorem. Moreover, several interesting results are derived from FLSoCFDEs in terms of the Mittage-Leffler function for both homogeneous and inhomogeneous cases. To understand the proposed technique, we solve a diffusion process problem (a biological model) and several mass-spring systems as applications. Their graphs are analyzed to illustrate and support the theoretical results.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7841249">Cited in <strong>8</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A34A05" title="MSC2020">34A05</a> </td> <td class="space"> Explicit solutions, first integrals of ordinary differential equations </td> </tr><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%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%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%3A47H10" title="MSC2020">47H10</a> </td> <td class="space"> Fixed-point theorems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A45D05" title="MSC2020">45D05</a> </td> <td class="space"> Volterra integral equations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Afuzzy+Caputo+%5C%28gH%5C%29-fractional+derivative">fuzzy Caputo $gH$-fractional derivative</a>; <a href="/?q=ut%3Atwo-dimensional+incommensurate+fuzzy+linear+systems+of+Caputo+fractional+differential+equations">two-dimensional incommensurate fuzzy linear systems of Caputo fractional differential equations</a>; <a href="/?q=ut%3AMittag-Leffler+function+involving+double+series">Mittag-Leffler function involving double series</a>; <a href="/?q=ut%3Acommensurate+and+incommensurate+fractional+order">commensurate and incommensurate fractional order</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 1542.34002" data-ciurl="/ci/07841249" data-biburl="/bibtex/07841249.bib" data-amsurl="/amsrefs/07841249.bib" data-xmlurl="/xml/07841249.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07841249.pdf" title="Zbl 1542.34002 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/10.1016/j.ins.2023.119372" aria-label="DOI for “Explicit analytical solutions of an incommensurate system of fractional differential equations in a fuzzy environment”" title="10.1016/j.ins.2023.119372">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">Dubois, D.; Prade, H., Towards fuzzy differential calculus part 3: differentiation, Fuzzy Sets Syst., 8, 3, 225-233 (1982) · <a href="/0499.28009" class="nowrap">Zbl 0499.28009</a></td> </tr><tr> <td>[2]</td> <td class="space">Puri, M. 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