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            <front>

                <journal-meta>
                                                                <journal-id>jum</journal-id>
            <journal-title-group>
                                                                                    <journal-title>Journal of Universal Mathematics</journal-title>
            </journal-title-group>
                            <issn pub-type="ppub">2618-5660</issn>
                                        <issn pub-type="epub">2618-5660</issn>
                                                                                            <publisher>
                    <publisher-name>Gökhan ÇUVALCIOĞLU</publisher-name>
                </publisher>
                    </journal-meta>
                <article-meta>
                                        <article-id pub-id-type="doi">10.33773/jum.1307156</article-id>
                                                                <article-categories>
                                            <subj-group  xml:lang="en">
                                                            <subject>Mathematical Sciences</subject>
                                                    </subj-group>
                                            <subj-group  xml:lang="tr">
                                                            <subject>Matematik</subject>
                                                    </subj-group>
                                    </article-categories>
                                                                                                                                                        <title-group>
                                                                                                                        <article-title>TWO POINT FUZZY BOUNDARY VALUE PROBLEM WITH EXTENSION PRINCIPLE USING HEAVISIDE FUNCTION</article-title>
                                                                                                                                        </title-group>
            
                                                    <contrib-group content-type="authors">
                                                                        <contrib contrib-type="author">
                                                                    <contrib-id contrib-id-type="orcid">
                                        https://orcid.org/0000-0002-3187-2800</contrib-id>
                                                                <name>
                                    <surname>Ceylan</surname>
                                    <given-names>Tahir</given-names>
                                </name>
                                                                    <aff>SİNOP ÜNİVERSİTESİ</aff>
                                                            </contrib>
                                                                                </contrib-group>
                        
                                        <pub-date pub-type="pub" iso-8601-date="20230731">
                    <day>07</day>
                    <month>31</month>
                    <year>2023</year>
                </pub-date>
                                        <volume>6</volume>
                                        <issue>2</issue>
                                        <fpage>131</fpage>
                                        <lpage>141</lpage>
                        
                        <history>
                                    <date date-type="received" iso-8601-date="20230530">
                        <day>05</day>
                        <month>30</month>
                        <year>2023</year>
                    </date>
                                                    <date date-type="accepted" iso-8601-date="20230728">
                        <day>07</day>
                        <month>28</month>
                        <year>2023</year>
                    </date>
                            </history>
                                        <permissions>
                    <copyright-statement>Copyright © 2018, Journal of Universal Mathematics</copyright-statement>
                    <copyright-year>2018</copyright-year>
                    <copyright-holder>Journal of Universal Mathematics</copyright-holder>
                </permissions>
            
                                                                                                <abstract><p>In this paper we deal with the fuzzy eigenfunctions of the two point fuzzy  boundary value problem (FBVP) with fuzzy coefficient of the boundary conditions. The fuzzy solution is obtained from the Zadeh&#039;s extension principle using the Heaviside function. The eigenvalues and the fuzzy eigenfunctions of the boundary value problem are found using the Wronskian functions. We present an example in order to compare the proposed solution.</p></abstract>
                                                                                    
            
                                                            <kwd-group>
                                                    <kwd>Fuzzy boundary value problem</kwd>
                                                    <kwd>  eigenvalue</kwd>
                                                    <kwd>  fuzzy eigenfunction</kwd>
                                                    <kwd>  Zadeh extension principle</kwd>
                                                    <kwd>  Heaviside function</kwd>
                                            </kwd-group>
                                                        
                                                                                                                                                    </article-meta>
    </front>
    <back>
                            <ref-list>
                                    <ref id="ref1">
                        <label>1</label>
                        <mixed-citation publication-type="journal">S.L. Chang, L.A. Zadeh, On Fuzzy Mapping and Control , IEEE Transactions on Systems Man Cybernetics, Vol. 2, No. 1, pp. 30-34 (1972).</mixed-citation>
                    </ref>
                                    <ref id="ref2">
                        <label>2</label>
                        <mixed-citation publication-type="journal">M. L. Puri, D. A. Ralescu , Differentials of fuzzy functions, Journal of Math. Analysis and App., Vol. 91, No. 2, pp. 552–558 (1983).</mixed-citation>
                    </ref>
                                    <ref id="ref3">
                        <label>3</label>
                        <mixed-citation publication-type="journal">O. Kaleva , Fuzzy differential equations, Fuzzy sets and systems, Vol. 24, No. 3, pp. 301–317 (1987).</mixed-citation>
                    </ref>
                                    <ref id="ref4">
                        <label>4</label>
                        <mixed-citation publication-type="journal">B. Bede, S. G. Gal , Generalizations of the differentiability of fuzzy number-valued functions with applications to fuzzy differential equations, Fuzzy Sets and Systems, Vol. 151, pp. 581-599 (2005).</mixed-citation>
                    </ref>
                                    <ref id="ref5">
                        <label>5</label>
                        <mixed-citation publication-type="journal">N. Gasilov, S.E. Amrahov, A.G. Fatullayev , Solution of linear differential equations with fuzzy boundary values, Fuzzy Sets Syst., Vol. 257, pp. 169–183 (2014).</mixed-citation>
                    </ref>
                                    <ref id="ref6">
                        <label>6</label>
                        <mixed-citation publication-type="journal">M.T. Mizukoshi, L.C. Barros, Y. Chalco-Cano, H. Rom´an-Flores, R.C. Bassanezi, Fuzzy differential equations and the extension principle, Inf. Sci., Vol. 177, pp. 3627–3635 (2007).</mixed-citation>
                    </ref>
                                    <ref id="ref7">
                        <label>7</label>
                        <mixed-citation publication-type="journal">H.K. Liu , Comparison results of two-point fuzzy boundary value problems, International Journal of Computational and Mathematical Sciences, Vol. 5, No. 1, pp. 1-7 (2011).</mixed-citation>
                    </ref>
                                    <ref id="ref8">
                        <label>8</label>
                        <mixed-citation publication-type="journal">H. Gultekin Citil, , The eigenvalues and the eigenfunctions of the Sturm- Liouville fuzzy boundary value problem according to the generalized differentiability, Scholars Journal of Physics, Vol. 4, No. 4, pp. 185–195 (2017).</mixed-citation>
                    </ref>
                                    <ref id="ref9">
                        <label>9</label>
                        <mixed-citation publication-type="journal">T. Ceylan, N. Altinisik, Eigenvalue problem with fuzzy coefficients of boundary conditions, Scholars Journal of Physics, Mathematics and Statistics, Vol. 5, No. 2, pp. 187–193 (2018).</mixed-citation>
                    </ref>
                                    <ref id="ref10">
                        <label>10</label>
                        <mixed-citation publication-type="journal">J.J. Buckley, T. Feuring , Fuzzy initial value problem for N-th order linear differential equations, Fuzzy Sets and Systems, Vol. 121, pp. 247–255 (2001).</mixed-citation>
                    </ref>
                                    <ref id="ref11">
                        <label>11</label>
                        <mixed-citation publication-type="journal">O. Akın, T. Khaniyev, S. Bayeg, I.B. Turksen, Solving a Second Order Fuzzy Initial Value Problem Using The Heaviside Function, Turk. J. Math. Comput. Sci., Vol. 4, pp. 16–25 (2016).</mixed-citation>
                    </ref>
                                    <ref id="ref12">
                        <label>12</label>
                        <mixed-citation publication-type="journal">G. Klir, B. Yuan, Fuzzy Sets and Fuzzy Logic,Prentice Hall Inc., Upper Saddle River, (1995).</mixed-citation>
                    </ref>
                                    <ref id="ref13">
                        <label>13</label>
                        <mixed-citation publication-type="journal">I. Sadeqi, M. Moradlou, M. Salehi, On approximate cauchy equation in felbin’s type fuzzy normed linear spaces, Iranian Journal of Fuzzy Sys., Vol. 10, No. 3, pp. 51-63 (2013).</mixed-citation>
                    </ref>
                                    <ref id="ref14">
                        <label>14</label>
                        <mixed-citation publication-type="journal">P. Diamond, P. Kloeden, Metric spaces of fuzzy sets, World Scientific, Singapore, (1994).</mixed-citation>
                    </ref>
                                    <ref id="ref15">
                        <label>15</label>
                        <mixed-citation publication-type="journal">A. Kandel, W. Byatt, Fuzzy differential equations,Proceedings of the International Conference on Cybernetics and Society,, Tokyo, (1978).</mixed-citation>
                    </ref>
                                    <ref id="ref16">
                        <label>16</label>
                        <mixed-citation publication-type="journal">L. C. de Barros, R. C. Bassanezi, P. A. Tonelli, On the continuity of the zadeh’s extension, In: Proceedings of Seventh IFSA World Congress, (1977).</mixed-citation>
                    </ref>
                                    <ref id="ref17">
                        <label>17</label>
                        <mixed-citation publication-type="journal">E. C. Titchmarsh, Eigenfunction expansions associated with second-order differential equations I, 2nd edn., Oxford University Press, London, (1962).</mixed-citation>
                    </ref>
                            </ref-list>
                    </back>
    </article>
