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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.1501013</article-id>
                                                                <article-categories>
                                            <subj-group  xml:lang="en">
                                                            <subject>Operator Algebras and Functional Analysis</subject>
                                                    </subj-group>
                                            <subj-group  xml:lang="tr">
                                                            <subject>Operatör Cebirleri ve Fonksiyonel Analiz</subject>
                                                    </subj-group>
                                    </article-categories>
                                                                                                                                                        <title-group>
                                                                                                                                                            <article-title>ON GENERALIZED CONFORMABLE FRACTIONAL OPERATORS</article-title>
                                                                                                    </title-group>
            
                                                    <contrib-group content-type="authors">
                                                                        <contrib contrib-type="author">
                                                                    <contrib-id contrib-id-type="orcid">
                                        https://orcid.org/0009-0000-2472-5311</contrib-id>
                                                                <name>
                                    <surname>Ermeydan Çiriş</surname>
                                    <given-names>Sümeyye</given-names>
                                </name>
                                                                    <aff>Kahramanmaraş üniversitesi</aff>
                                                            </contrib>
                                                    <contrib contrib-type="author">
                                                                    <contrib-id contrib-id-type="orcid">
                                        https://orcid.org/0000-0001-8855-9260</contrib-id>
                                                                <name>
                                    <surname>Yıldırım</surname>
                                    <given-names>Huseyin</given-names>
                                </name>
                                                                    <aff>KAHRAMANMARAS SUTCU IMAM UNIVERSITY</aff>
                                                            </contrib>
                                                                                </contrib-group>
                        
                                        <pub-date pub-type="pub" iso-8601-date="20250131">
                    <day>01</day>
                    <month>31</month>
                    <year>2025</year>
                </pub-date>
                                        <volume>8</volume>
                                        <issue>1</issue>
                                        <fpage>1</fpage>
                                        <lpage>19</lpage>
                        
                        <history>
                                    <date date-type="received" iso-8601-date="20240624">
                        <day>06</day>
                        <month>24</month>
                        <year>2024</year>
                    </date>
                                                    <date date-type="accepted" iso-8601-date="20250128">
                        <day>01</day>
                        <month>28</month>
                        <year>2025</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 introduce the concepts of left and right generalized conformable fractional integrals, alongside the corresponding derivatives.Additionally, we extend our investigation to derive the generalized conformable derivatives for functions within specific spaces, elucidating their inherent properties.</p></abstract>
                                                            
            
                                                                                        <kwd-group>
                                                    <kwd>conformable derivatives</kwd>
                                                    <kwd>  conformable integrals</kwd>
                                                    <kwd>  fractional derivatives</kwd>
                                                    <kwd>  fractional integrals.</kwd>
                                            </kwd-group>
                            
                                                                                                                                                    </article-meta>
    </front>
    <back>
                            <ref-list>
                                    <ref id="ref1">
                        <label>1</label>
                        <mixed-citation publication-type="journal">F. Jarad, E. Ugurlu, T. Abdeljawad, D. Baleanu, On a new class of fractional operators, Advance in Di_erence Equations, Vol.247, (2017).</mixed-citation>
                    </ref>
                                    <ref id="ref2">
                        <label>2</label>
                        <mixed-citation publication-type="journal">K. Diethelm, The Analysis of Fractional Di_erential Equations, Lecture Notes in Mathematics, (2010).</mixed-citation>
                    </ref>
                                    <ref id="ref3">
                        <label>3</label>
                        <mixed-citation publication-type="journal">R. Hilfer, Applications of Fractional Calculus in Physics, Word Scienti_c, Singapore, (2000).</mixed-citation>
                    </ref>
                                    <ref id="ref4">
                        <label>4</label>
                        <mixed-citation publication-type="journal">A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Application of Fractional Differential Equations, North-Holland Matematics Studies, Vol. 204 (2006).</mixed-citation>
                    </ref>
                                    <ref id="ref5">
                        <label>5</label>
                        <mixed-citation publication-type="journal">R.L. Magin, Fractional Calculus in Bioengineering, Begell House Publishers, Redding, (2006).</mixed-citation>
                    </ref>
                                    <ref id="ref6">
                        <label>6</label>
                        <mixed-citation publication-type="journal">I. Podlubny, Fractional Di_erential Equations, Academic Press, San Diego, (1999).</mixed-citation>
                    </ref>
                                    <ref id="ref7">
                        <label>7</label>
                        <mixed-citation publication-type="journal">S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon &amp; Breach, Yverdon, (1993).</mixed-citation>
                    </ref>
                                    <ref id="ref8">
                        <label>8</label>
                        <mixed-citation publication-type="journal">U.N. Katugampola, New approach to generalized fractional integral, Appl. Math. Comput., Vol.218, pp.860-865, (2011).</mixed-citation>
                    </ref>
                                    <ref id="ref9">
                        <label>9</label>
                        <mixed-citation publication-type="journal">U.N Katugampola, A new approach to generalized fractional derivatives, Bull. Math. Anal. Appl., Vol.6, pp.1-15, (2014).</mixed-citation>
                    </ref>
                                    <ref id="ref10">
                        <label>10</label>
                        <mixed-citation publication-type="journal">T. Abdeljawad, On conformable fractional calculus, J.Comput. Appl. Math., Vol.279, pp.57-66, (2015).</mixed-citation>
                    </ref>
                                    <ref id="ref11">
                        <label>11</label>
                        <mixed-citation publication-type="journal">A.A Kilbas, Hadamard type fractional calculus, J. Korean Math. Soc., Vol.38, pp.1191-1204, (2001).</mixed-citation>
                    </ref>
                                    <ref id="ref12">
                        <label>12</label>
                        <mixed-citation publication-type="journal">Y.Y. Gambo, F. Jarad, T. Abdeljawad, D. Baleanu, On Caputo modi_cation of the Hadamard fractional derivate. Adv. Di_er.Equ., Vol.2014, No.10 (2014).</mixed-citation>
                    </ref>
                                    <ref id="ref13">
                        <label>13</label>
                        <mixed-citation publication-type="journal">F. Jarad, T. Abdeljawad, D. Baleanu, Caputo-type modi_cation of the Hadamard fractional derivative, Adv. Di_er. Equ., Vol.142 (2012).</mixed-citation>
                    </ref>
                                    <ref id="ref14">
                        <label>14</label>
                        <mixed-citation publication-type="journal">Y. Adjabi, F. Jarad, D. Baleanu, T. Abdeljawad, On Cauchy problems with Caputo Hadamard fractional derivatives, J.Comput. Anal. Appl., Vol.21, No.1, pp.661-681 (2016).</mixed-citation>
                    </ref>
                                    <ref id="ref15">
                        <label>15</label>
                        <mixed-citation publication-type="journal">F. Jarad, T. Abdeljawad, D. Baleanu, On the generalized fractional derivatives and their Caputo modi_cation. J., Nonlinear Sci. Appl., Vol.10, No.5, pp.2607-2619 (2017).</mixed-citation>
                    </ref>
                                    <ref id="ref16">
                        <label>16</label>
                        <mixed-citation publication-type="journal">A. Akkurt, H. Yıldırım, On Hermite-Hadamard-Fej_er type inequalities for convex functions via fractional integrals, Mathematica Moravica, Vol.21, No.1, pp.105-123 (2017).</mixed-citation>
                    </ref>
                                    <ref id="ref17">
                        <label>17</label>
                        <mixed-citation publication-type="journal">H. Yıldırım, Z. Kırtay, Ostrowski Inequality for Generalized Fractional Integral and Related Inequalities, Malaya Journal of Matematik, Vol.2, No.3, pp.322-329 (2014).</mixed-citation>
                    </ref>
                                    <ref id="ref18">
                        <label>18</label>
                        <mixed-citation publication-type="journal">T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math., Vol.279, pp.57- 66 (2015).</mixed-citation>
                    </ref>
                                    <ref id="ref19">
                        <label>19</label>
                        <mixed-citation publication-type="journal">L.G. Zivlaei, A.B. Mingarelli, On the Basic Theory of Some Generalized and Fractional Derivatives, Fractal and Fractional, Vol.6, No.672 (2022).</mixed-citation>
                    </ref>
                                    <ref id="ref20">
                        <label>20</label>
                        <mixed-citation publication-type="journal">M. Tarıq, K.S. Ntouyas, A.A. Shaikh, New variant of Hermite-Hadamard, Fej_er and Pachpatte-Type Inequality and Its Re_nements Pertaining to Fractional Integral operator, Fractal and Fractional, Vol.7, No.405 (2023).</mixed-citation>
                    </ref>
                                    <ref id="ref21">
                        <label>21</label>
                        <mixed-citation publication-type="journal">E. Kaçar, Z. Kaçar, H. Yıldırım, Integral inequalities for Riemann-Liouville Fractional Integral of a Function with Respeect to Another Function, Iran J. Matth Sci Inform. Vol.13, pp.1-13 (2018).</mixed-citation>
                    </ref>
                            </ref-list>
                    </back>
    </article>
