<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0035-001X</journal-id>
<journal-title><![CDATA[Revista mexicana de física]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. fis.]]></abbrev-journal-title>
<issn>0035-001X</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Física]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0035-001X2020000200187</article-id>
<article-id pub-id-type="doi">10.31349/revmexfis.66.187</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Analysis of fractional Duffing oscillator]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Eze]]></surname>
<given-names><![CDATA[S.C.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,University of Nigeria Department of Mathematics ]]></institution>
<addr-line><![CDATA[Nsukka ]]></addr-line>
<country>Nigeria</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>04</month>
<year>2020</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>04</month>
<year>2020</year>
</pub-date>
<volume>66</volume>
<numero>2</numero>
<fpage>187</fpage>
<lpage>191</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0035-001X2020000200187&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0035-001X2020000200187&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0035-001X2020000200187&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract In this contribution, a simple analytical method (which is an elegant combination of well known methods; perturbation and Laplace methods) for solving non-linear and non-homogeneous fractional differential equations is proposed. In particular, the proposed method was used to analyze the fractional Duffing oscillator. The technique employed can be used to analyze other non-linear fractional differential equations and can also be extended to non-linear partial fractional differential equations. The performance of this method is reliable, effective, and gives more general solutions.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Fractional calculus]]></kwd>
<kwd lng="en"><![CDATA[fractional Duffing oscillator]]></kwd>
<kwd lng="en"><![CDATA[analytical method]]></kwd>
<kwd lng="en"><![CDATA[02.30.Jr]]></kwd>
<kwd lng="en"><![CDATA[02.30.Vv]]></kwd>
<kwd lng="en"><![CDATA[41.20.Cv]]></kwd>
<kwd lng="en"><![CDATA[45.10.Hj]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<label>1</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ross]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
</person-group>
<source><![CDATA[Hist. Math.]]></source>
<year>1977</year>
<volume>4</volume>
<page-range>75</page-range></nlm-citation>
</ref>
<ref id="B2">
<label>2</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Al-Refai]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Ali Hajji]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Syam]]></surname>
<given-names><![CDATA[M. I.]]></given-names>
</name>
</person-group>
<source><![CDATA[Abstr. Appl. Anal.]]></source>
<year>2014</year>
<volume>2014</volume>
</nlm-citation>
</ref>
<ref id="B3">
<label>3</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Eze]]></surname>
<given-names><![CDATA[S. C.]]></given-names>
</name>
<name>
<surname><![CDATA[Oyesanya]]></surname>
<given-names><![CDATA[M.O.]]></given-names>
</name>
</person-group>
<source><![CDATA[J. Fract. Cal. Appl.]]></source>
<year>2019</year>
<volume>10</volume>
<page-range>10</page-range></nlm-citation>
</ref>
<ref id="B4">
<label>4</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Eze]]></surname>
<given-names><![CDATA[S. C.]]></given-names>
</name>
<name>
<surname><![CDATA[Oyesanya]]></surname>
<given-names><![CDATA[M.O.]]></given-names>
</name>
</person-group>
<source><![CDATA[Math. Clim. Weather Forecast.]]></source>
<year>2019</year>
<volume>5</volume>
<page-range>1</page-range></nlm-citation>
</ref>
<ref id="B5">
<label>5</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mohamed]]></surname>
<given-names><![CDATA[A.E.]]></given-names>
</name>
<name>
<surname><![CDATA[Amnah]]></surname>
<given-names><![CDATA[S.A.]]></given-names>
</name>
</person-group>
<source><![CDATA[J. Fract. Calc. Appl.]]></source>
<year>2013</year>
<volume>4</volume>
<page-range>357</page-range></nlm-citation>
</ref>
<ref id="B6">
<label>6</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ahmet]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Özkan]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Ali]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Anjan]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
</person-group>
<source><![CDATA[Romaninan J. Phys.]]></source>
<year>2014</year>
<volume>60</volume>
<page-range>360</page-range></nlm-citation>
</ref>
<ref id="B7">
<label>7</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Djurdjica]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Arpal]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Aleresandur]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<source><![CDATA[TWMS J. App. Eng. Math.]]></source>
<year>2014</year>
<volume>4</volume>
<page-range>98</page-range></nlm-citation>
</ref>
<ref id="B8">
<label>8</label><nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rand]]></surname>
<given-names><![CDATA[R. H.]]></given-names>
</name>
<name>
<surname><![CDATA[Sah]]></surname>
<given-names><![CDATA[S. M.]]></given-names>
</name>
<name>
<surname><![CDATA[Suchorsky]]></surname>
<given-names><![CDATA[M. K.]]></given-names>
</name>
</person-group>
<source><![CDATA[]]></source>
<year>2010</year>
<conf-name><![CDATA[ Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Montreal]]></conf-name>
<conf-date>2010</conf-date>
<conf-loc>New York </conf-loc>
<page-range>873</page-range></nlm-citation>
</ref>
<ref id="B9">
<label>9</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Yin]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
</person-group>
<source><![CDATA[Appl. Math.]]></source>
<year>2013</year>
<volume>4</volume>
<page-range>113</page-range></nlm-citation>
</ref>
<ref id="B10">
<label>10</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Pranay]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Rubayyi]]></surname>
<given-names><![CDATA[T.A.]]></given-names>
</name>
</person-group>
<source><![CDATA[J. Nonlinear Sci. Appl.]]></source>
<year>2016</year>
<volume>9</volume>
</nlm-citation>
</ref>
<ref id="B11">
<label>11</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Oyesanya]]></surname>
<given-names><![CDATA[M. O.]]></given-names>
</name>
</person-group>
<source><![CDATA[Trans. Of NAMP]]></source>
<year>2015</year>
<volume>1</volume>
<page-range>133</page-range></nlm-citation>
</ref>
<ref id="B12">
<label>12</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Jafari]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Khalique]]></surname>
<given-names><![CDATA[C.M.]]></given-names>
</name>
<name>
<surname><![CDATA[Nazari]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Appl. Math. Lett.]]></source>
<year>2011</year>
<volume>24</volume>
</nlm-citation>
</ref>
<ref id="B13">
<label>13</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Okasha]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Nady]]></surname>
<given-names><![CDATA[El]]></given-names>
</name>
<name>
<surname><![CDATA[Lashin]]></surname>
<given-names><![CDATA[M. M. A.]]></given-names>
</name>
</person-group>
<source><![CDATA[J. Mech. Eng. Autom.]]></source>
<year>2016</year>
<volume>6</volume>
<page-range>110</page-range></nlm-citation>
</ref>
<ref id="B14">
<label>14</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Venkatesh]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Subhadeep]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Asok]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Signal Process.]]></source>
<year>2008</year>
<volume>88</volume>
<page-range>339</page-range></nlm-citation>
</ref>
<ref id="B15">
<label>15</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rosales]]></surname>
<given-names><![CDATA[J. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Gómez]]></surname>
<given-names><![CDATA[J. F.]]></given-names>
</name>
<name>
<surname><![CDATA[Guia]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Tkach]]></surname>
<given-names><![CDATA[V. I.]]></given-names>
</name>
<name>
<surname><![CDATA[Sukhoivanov]]></surname>
<given-names><![CDATA[I. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Shulika]]></surname>
<given-names><![CDATA[O. V.]]></given-names>
</name>
</person-group>
<source><![CDATA[Proceedings of the 11th International Conference on Laser and Fiber-Optical Networks Modeling, Kharkov, 2011]]></source>
<year>2011</year>
<page-range>1</page-range><publisher-loc><![CDATA[Kharkov ]]></publisher-loc>
<publisher-name><![CDATA[IEEE]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B16">
<label>16</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gomez Aguilar]]></surname>
<given-names><![CDATA[J. F.]]></given-names>
</name>
<name>
<surname><![CDATA[Rosales]]></surname>
<given-names><![CDATA[J. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Bernal-Alvarado]]></surname>
<given-names><![CDATA[J.J.]]></given-names>
</name>
<name>
<surname><![CDATA[Cordova-Fraga]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Guzmán-Cabrera]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Rev. Mex. Fis.]]></source>
<year>2012</year>
<volume>58</volume>
<page-range>348</page-range></nlm-citation>
</ref>
<ref id="B17">
<label>17</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bojanic]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Seneta]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<source><![CDATA[J. Math. Anal. Appl.]]></source>
<year>1971</year>
<volume>34</volume>
<page-range>302</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
