<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.4 20241031//EN"
        "https://jats.nlm.nih.gov/publishing/1.4/JATS-journalpublishing1-4.dtd">
<article  article-type="research-article"        dtd-version="1.4">
            <front>

                <journal-meta>
                                                                <journal-id>saujs</journal-id>
            <journal-title-group>
                                                                                    <journal-title>Sakarya University Journal of Science</journal-title>
            </journal-title-group>
                                        <issn pub-type="epub">2147-835X</issn>
                                                                                            <publisher>
                    <publisher-name>Sakarya University</publisher-name>
                </publisher>
                    </journal-meta>
                <article-meta>
                                        <article-id pub-id-type="doi">10.16984/saufenbilder.282553</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>On the oscillation of fractional order nonlinear differential equations</article-title>
                                                                                                                                                                                                <trans-title-group xml:lang="tr">
                                    <trans-title>Kesirli mertebeden doğrusal olmayan diferensiyel denklemlerin salınımlılığı üzerine</trans-title>
                                </trans-title-group>
                                                                                                    </title-group>
            
                                                    <contrib-group content-type="authors">
                                                                        <contrib contrib-type="author">
                                                                <name>
                                    <surname>Bayram</surname>
                                    <given-names>Mustafa</given-names>
                                </name>
                                                                    <aff>İSTANBUL GELİŞİM ÜNİVERSİTESİ</aff>
                                                            </contrib>
                                                    <contrib contrib-type="author">
                                                                <name>
                                    <surname>Seçer</surname>
                                    <given-names>Aydın</given-names>
                                </name>
                                                                    <aff>YILDIZ TEKNIK UNIV</aff>
                                                            </contrib>
                                                    <contrib contrib-type="author">
                                                                <name>
                                    <surname>Adıgüzel</surname>
                                    <given-names>Hakan</given-names>
                                </name>
                                                                    <aff>YILDIZ TEKNIK UNIV</aff>
                                                            </contrib>
                                                                                </contrib-group>
                        
                                        <pub-date pub-type="pub" iso-8601-date="20171201">
                    <day>12</day>
                    <month>01</month>
                    <year>2017</year>
                </pub-date>
                                        <volume>21</volume>
                                        <issue>6</issue>
                                        <fpage>1512</fpage>
                                        <lpage>1523</lpage>
                        
                        <history>
                                    <date date-type="received" iso-8601-date="20161230">
                        <day>12</day>
                        <month>30</month>
                        <year>2016</year>
                    </date>
                                                    <date date-type="accepted" iso-8601-date="20171016">
                        <day>10</day>
                        <month>16</month>
                        <year>2017</year>
                    </date>
                            </history>
                                        <permissions>
                    <copyright-statement>Copyright © 1997, Sakarya University Journal of Science</copyright-statement>
                    <copyright-year>1997</copyright-year>
                    <copyright-holder>Sakarya University Journal of Science</copyright-holder>
                </permissions>
            
                                                                                                <abstract><p>In the article, we are concerned with the oscillatory solutionsof a class of fractional differential equations. By using generalized Riccatifunction and Hardy inequalities, we present some oscillation criterias. As aresult we give some examples that validity of the established results.</p></abstract>
                                                                                                                                    <trans-abstract xml:lang="tr">
                            <p>Bu makalede, kesirli mertebeden diferensiyel denklemlerin birsınıfının salınımlı çözümleriyle ilgilenildi. Genelleştirilmiş Riccatifonksiyonu ve Hardy eşitsizlikleri kullanılarak, baz salınımlılık kriterlerisunuldu. Sonuç olarak, kurulan sonuçları sağlayan bazı örnekler verildi.</p></trans-abstract>
                                                            
            
                                                            <kwd-group>
                                                    <kwd>Oscillation</kwd>
                                                    <kwd>  Oscillation Criterias</kwd>
                                                    <kwd>  Fractional Derivative</kwd>
                                                    <kwd>  Generalized Riccati Function</kwd>
                                            </kwd-group>
                                                        
                                                                            <kwd-group xml:lang="tr">
                                                    <kwd>Salınımlılık</kwd>
                                                    <kwd>  Salınımlılık Kriterleri</kwd>
                                                    <kwd>  Kesirli Türev</kwd>
                                                    <kwd>  Genelleştirilmiş Riccati Fonksiyonu</kwd>
                                            </kwd-group>
                                                                                                            </article-meta>
    </front>
    <back>
                            <ref-list>
                                    <ref id="ref1">
                        <label>1</label>
                        <mixed-citation publication-type="journal">Das, S., Functional Fractional Calculus for System Identification and Controls, Springer, New York (2008).</mixed-citation>
                    </ref>
                                    <ref id="ref2">
                        <label>2</label>
                        <mixed-citation publication-type="journal">Diethelm, K., Freed, A., On the solution of nonlinear fractional order differential equations used in the modeling of viscoplasticity, In: Keil, F, Mackens, W, Vob, H, Werther, J (eds.) Scientific Computing in Chemical Engineering II: Computational Fluid Dynamics, Reaction Engineering and Molecular Properties, pp. 217-224. Springer, Heidelberg (1999)</mixed-citation>
                    </ref>
                                    <ref id="ref3">
                        <label>3</label>
                        <mixed-citation publication-type="journal">Metzler, R., Schick, W., Kilian, H., Nonnenmacher, T., (1995). Relaxation in filled polymers: a fractional calculus approach, J. Chem. Phys. 103, 7180-7186.</mixed-citation>
                    </ref>
                                    <ref id="ref4">
                        <label>4</label>
                        <mixed-citation publication-type="journal">Diethelm, K., The Analysis of Fractional Differential Equations, Springer, Berlin (2010).</mixed-citation>
                    </ref>
                                    <ref id="ref5">
                        <label>5</label>
                        <mixed-citation publication-type="journal">Miller, K., Ross, B., An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York (1993).</mixed-citation>
                    </ref>
                                    <ref id="ref6">
                        <label>6</label>
                        <mixed-citation publication-type="journal">Podlubny, I., Fractional Differential Equations, Academic Press, San Diego (1999).</mixed-citation>
                    </ref>
                                    <ref id="ref7">
                        <label>7</label>
                        <mixed-citation publication-type="journal">Kilbas, A., Srivastava, H., Trujillo, J., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam (2006).</mixed-citation>
                    </ref>
                                    <ref id="ref8">
                        <label>8</label>
                        <mixed-citation publication-type="journal">Sun, S., Zhao, Y., Han, Z., Li, Y.,(2012). The existence of solutions for boundary value problem of fractional hybrid differential equations, Communications in Nonlinear Science and Numerical Simulation, 17(12), 4961-4967.</mixed-citation>
                    </ref>
                                    <ref id="ref9">
                        <label>9</label>
                        <mixed-citation publication-type="journal">Muslim, M., (2009). Existence and approximation of solutions to fractional differential equations, Math. Comput. Model. 49, 1164-1172.</mixed-citation>
                    </ref>
                                    <ref id="ref10">
                        <label>10</label>
                        <mixed-citation publication-type="journal">Saadatmandi, A., Dehghan, M., (2010). A new operational matrix for solving fractional-order differential equations, Comput. Math. Appl. 59, 1326-1336.</mixed-citation>
                    </ref>
                                    <ref id="ref11">
                        <label>11</label>
                        <mixed-citation publication-type="journal">Trigeassou, J., Maamri, N., Sabatier, J., Oustaloup, A., (2011). A Lyapunov approach to the stability of fractional differential equations, Signal Process. 91, 437-445.</mixed-citation>
                    </ref>
                                    <ref id="ref12">
                        <label>12</label>
                        <mixed-citation publication-type="journal">Deng, W., (2010). Smoothness and stability of the solutions for nonlinear fractional differential equations. Nonlinear Anal. 72, 1768-1777.</mixed-citation>
                    </ref>
                                    <ref id="ref13">
                        <label>13</label>
                        <mixed-citation publication-type="journal">Ogrekci, S., (2015). Generalized Taylor Series Method for Solving Nonlinear Fractional Differential Equations with Modi_ed Riemann-Liouville Derivative, Advances in Mathematical Physics, 2015, 1-10.</mixed-citation>
                    </ref>
                                    <ref id="ref14">
                        <label>14</label>
                        <mixed-citation publication-type="journal">Grace, S., Agarwal, R., Wong, P., Zafer, A., (2012). On the oscillation of fractional differential equations. Fractional Calculus and Applied Analysis, 15(2), 222-231.</mixed-citation>
                    </ref>
                                    <ref id="ref15">
                        <label>15</label>
                        <mixed-citation publication-type="journal">Parhi, N., (2011). Oscillation and non-oscillation of solutions of second order difference equations involving generalized difference, Appl. Math. Comput. 218(2011), 458-468.</mixed-citation>
                    </ref>
                                    <ref id="ref16">
                        <label>16</label>
                        <mixed-citation publication-type="journal">Li, W. N., (2015). Forced oscillation criteria for a class of fractional partial differential equations with damping term, Mathematical Problems in Engineering, 2015</mixed-citation>
                    </ref>
                                    <ref id="ref17">
                        <label>17</label>
                        <mixed-citation publication-type="journal">Prakash, P., Harikrishnan, S., (2012). Oscillation of solutions of impulsive vector hyperbolic differential equations with delays, Appl. Anal. 91, 459-473.</mixed-citation>
                    </ref>
                                    <ref id="ref18">
                        <label>18</label>
                        <mixed-citation publication-type="journal">Sagayaraj, M. R., Selvam, A. G. M., Loganathan, M. P.,(2014). Oscillation criteria for a class of discrete nonlinear fractional equations, Bull. Soc. Math. Serv. Stand., 3 27-35.</mixed-citation>
                    </ref>
                                    <ref id="ref19">
                        <label>19</label>
                        <mixed-citation publication-type="journal">Secer, A., Adiguzel, H., (2016). Oscillation of solutions for a class of nonlinear fractional difference equations. The Journal of Nonlinear Science and Applications (JNSA), 9(11), 5862-5869.</mixed-citation>
                    </ref>
                                    <ref id="ref20">
                        <label>20</label>
                        <mixed-citation publication-type="journal">Li, W. N., (2016). Oscillation results for certain forced fractional difference equations with damping term, Advances in Difference Equations, 1, 1-9.</mixed-citation>
                    </ref>
                                    <ref id="ref21">
                        <label>21</label>
                        <mixed-citation publication-type="journal">Ogrekci, S., (2015). New interval oscillation criteria for second-order functional differential equations with nonlinear damping, Open Mathematics, 13, 239-246.</mixed-citation>
                    </ref>
                                    <ref id="ref22">
                        <label>22</label>
                        <mixed-citation publication-type="journal">Sun, Y., Kong, Q., (2011). Interval criteria for forced oscillation with nonlinearities given by Riemann-Stieltjes integrals, Comput. Math. Appl. 62, 243-252.</mixed-citation>
                    </ref>
                                    <ref id="ref23">
                        <label>23</label>
                        <mixed-citation publication-type="journal">Grace, S. R., Graef J. R., and El-Beltagy, M. A., (2012). On the oscillation of third order neutral delay dynamic equations on time scales, Computers and Mathematics with Applications, 63(4), 775{782.</mixed-citation>
                    </ref>
                                    <ref id="ref24">
                        <label>24</label>
                        <mixed-citation publication-type="journal">Agarwal, R. P., Bohner, M., and Saker, S. H., (2005). Oscillation of second order delay dynamic equations, Canadian Applied Mathematics Quarterly, 13(1), 1-18.</mixed-citation>
                    </ref>
                                    <ref id="ref25">
                        <label>25</label>
                        <mixed-citation publication-type="journal">Zheng, B., (2013). Oscillation for a class of nonlinear fractional differential equations with damping term, Journal of Advanced Mathematical Studies 6.1, 107-109.</mixed-citation>
                    </ref>
                                    <ref id="ref26">
                        <label>26</label>
                        <mixed-citation publication-type="journal">Qin, H., Zheng, B., (2013). Oscillation of a class of fractional differential equations with damping term. Sci. World J. 2013, Article ID 685621.</mixed-citation>
                    </ref>
                                    <ref id="ref27">
                        <label>27</label>
                        <mixed-citation publication-type="journal">Liu, T., Zheng, B., Meng, F., (2013). Oscillation on a class of differential equations of fractional order, Mathematical Problems in Engineering, 2013.</mixed-citation>
                    </ref>
                                    <ref id="ref28">
                        <label>28</label>
                        <mixed-citation publication-type="journal">Bayram, M., Adiguzel, H., Ogrekci, S., (2015). Oscillation of fractional order functional differential equations with nonlinear damping, Open Physics, 13(1).</mixed-citation>
                    </ref>
                                    <ref id="ref29">
                        <label>29</label>
                        <mixed-citation publication-type="journal">Feng, Q., (2014). Oscillatory Criteria For Two Fractional Differential Equations, WSEAS Transactions on Mathematics, 13 800-810.</mixed-citation>
                    </ref>
                                    <ref id="ref30">
                        <label>30</label>
                        <mixed-citation publication-type="journal">Bayram, M., Adiguzel, H., Secer, A., (2016). Oscillation criteria for nonlinear fractional differential equation with damping term, Open Physics,14(1), 119-128.</mixed-citation>
                    </ref>
                                    <ref id="ref31">
                        <label>31</label>
                        <mixed-citation publication-type="journal">Ogrekci, S., (2015). Interval oscillation criteria for functional differential equations of fractional order, Advances in Difference Equations, 2015(1).</mixed-citation>
                    </ref>
                                    <ref id="ref32">
                        <label>32</label>
                        <mixed-citation publication-type="journal">Jumarie, G.,(2006). Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results. Comput. Math. Appl. 51, 1367-1376.</mixed-citation>
                    </ref>
                                    <ref id="ref33">
                        <label>33</label>
                        <mixed-citation publication-type="journal">Jumarie, G., (2009). Table of some basic fractional calculus formulae derived froma modified Riemann-Liouville derivative for nondifferentiable functions, Applied Mathematics Letters, 22(3), 378-385.</mixed-citation>
                    </ref>
                                    <ref id="ref34">
                        <label>34</label>
                        <mixed-citation publication-type="journal">Lu, B., (2012). Backlund transformation of fractional Riccati equation and its applications to nonlinear fractional partial differential equations, Physics Letters A, vol. 376, no. 28-29, 2045-2048.</mixed-citation>
                    </ref>
                                    <ref id="ref35">
                        <label>35</label>
                        <mixed-citation publication-type="journal">Faraz, N., Khan, Y., Jafari, H., Yildirim, A., and Madani, M., (2011). Fractional variational iteration method via modified Riemann-Liouville derivative, Journal of King Saud University-Science, 23(4), 413-417.</mixed-citation>
                    </ref>
                                    <ref id="ref36">
                        <label>36</label>
                        <mixed-citation publication-type="journal">Hardy, G. H., Littlewood, J. E., Polya, G., Inequalities, 2nd edn. Cambridge University Press, Cambridge, (1988).</mixed-citation>
                    </ref>
                            </ref-list>
                    </back>
    </article>
