<?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>S0035-001X2018000500539</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Coupled reaction-diffusion waves in a chemical system via fractional derivatives in Liouville-Caputo sense]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Saad]]></surname>
<given-names><![CDATA[Khaled M.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
<xref ref-type="aff" rid="Aaf"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Gómez-Aguilar]]></surname>
<given-names><![CDATA[J.F.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Najran University Faculty of Arts and Sciences Department of Mathematics]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Saudi Arabia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Taiz University College of Applied Science Department of Mathematics]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Yemen</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Tecnológico Nacional de México/CENIDET  ]]></institution>
<addr-line><![CDATA[Cuernavaca Morelos]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>10</month>
<year>2018</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>10</month>
<year>2018</year>
</pub-date>
<volume>64</volume>
<numero>5</numero>
<fpage>539</fpage>
<lpage>547</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0035-001X2018000500539&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0035-001X2018000500539&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0035-001X2018000500539&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract In this paper, we have generalized the fractional cubic isothermal auto-catalytic chemical system (FCIACS) with Liouville-Caputo, Caputo- Fabrizio-Caputo, and Atangana-Baleanu-Caputo fractional time derivatives, respectively. We apply the Homotopy Analysis Transform Method (HATM) to compute the approximate solutions of FCIACS using these fractional derivatives. We study the convergence analysis of HATM by computing the residual error function. Also, we find the optimal values of h so we assure the convergence of the approximate solutions. Finally we show the behavior of the approximate solutions graphically. The results obtained are very effectiveness and accuracy. 2010 Mathematics Subject Classification: 34A34, 35R11, 65M12, 26A33, 34A08, 35-XX.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Fractional isothermal auto-catalytic chemical systems]]></kwd>
<kwd lng="en"><![CDATA[HATM]]></kwd>
<kwd lng="en"><![CDATA[Liouville-Caputo fractional derivative]]></kwd>
<kwd lng="en"><![CDATA[Caputo-Fabrizio fractional derivative]]></kwd>
<kwd lng="en"><![CDATA[Atangana-Baleanu fractional derivative]]></kwd>
<kwd lng="en"><![CDATA[h-curves]]></kwd>
<kwd lng="en"><![CDATA[02.30.Jr]]></kwd>
<kwd lng="en"><![CDATA[03.65.Fd]]></kwd>
<kwd lng="en"><![CDATA[04.20.Jb]]></kwd>
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