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    <title>International Journal of Partial Differential Equations and Applications</title>
    <link>http://www.sciepub.com/journal/IJPDEA</link>
    <description>International Journal of Partial Differential Equations and Applications is a quarterly international journal that publishes original research papers of high quality in all areas related to partial differential equations and their applications in biology, economics, engineering, physics, mathematics and other related areas of science. Papers addressing new theoretical techniques, novel ideas, and new analysis tools are suitable topics for the journal. The International Journal of Partial Differential Equations and Applications publishes research and review articles focused on the application of partial differential equations, as well as review articles related to all aspects of partial differential equations.</description>
    <dc:publisher>Science and Education Publishing</dc:publisher>
		<dc:language>en</dc:language>
		<dc:rights>2013 Science and Education Publishing Co. Ltd All rights reserved.</dc:rights>
		<prism:publicationName>International Journal of Partial Differential Equations and Applications</prism:publicationName>
		9
		1
		January 2022
		<prism:copyright>2013 Science and Education Publishing Co. Ltd All rights reserved.</prism:copyright>
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<title>
Solutions of Balance-Transport Models for (Solid-State Fermentation) Bioreactors with Infinite Diffusion
</title>
<link>http://pubs.sciepub.com/ijpdea/9/1/1</link>
<description>
<![CDATA[The models used to examine the processes of the solid-state fermentation bioreactors can be improved using the heat and mass transfer models compared to empirical models. This study examines the oxygen balance equations, water balance and energy balance equations for solid-state fermentation bioreactors. For the precise study of these important transport problems some advanced ingredients of applied mathematics such as sobolev spaces, weak solutions, Galerkin method, Gronwall's inequality and Harnack's inequality has been used. Based upon these concepts, the solutions of the balance equations for bioreactors is presented. By the proposed method, the uniqueness of the solutions of the balance equations has been proved. This procedure leads to a general methodology for reducing these initial/boundary partial differential equations to a system of ordinary differential equations which easily can be solved. It is also shown in this structure that the solution is the best answer since it supports the infinite diffusion speed of disturbances.]]>
</description>
<dc:creator>
Atefeh  Hasan-Zadeh
</dc:creator>
<dc:date>2022-05-17</dc:date>
<dc:publisher>Science and Education Publishing</dc:publisher>
<prism:publicationDate>2022-05-17</prism:publicationDate>
<prism:number>1</prism:number>
<prism:volume>9</prism:volume>
<prism:startingPage>1</prism:startingPage>
<prism:endingPage>6</prism:endingPage>
<prism:doi>10.12691/ijpdea-9-1-1</prism:doi>
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<item rdf:about="http://pubs.sciepub.com/ijpdea/9/1/2">
<title>
Review on Different Special Functions in Fractional Calculus
</title>
<link>http://pubs.sciepub.com/ijpdea/9/1/2</link>
<description>
<![CDATA[In this paper, we reviewed the specific tasks involved in solving different mathematical equations or fractional integral. Since solutions for different component of modeling models from various fields such as physics, engineering, chemistry, biological etc. involve special work as part of their solutions, here, we review and include the type and general- ization of such specialized functions.]]>
</description>
<dc:creator>
Bhaktaraj  Thiyam, Konthoujam  Ibochouba Singh, Md.  Indraman Khan, Md.  Mazhar Ul Haque, R.K  Pratima Devi
</dc:creator>
<dc:date>2022-12-22</dc:date>
<dc:publisher>Science and Education Publishing</dc:publisher>
<prism:publicationDate>2022-12-22</prism:publicationDate>
<prism:number>1</prism:number>
<prism:volume>9</prism:volume>
<prism:startingPage>7</prism:startingPage>
<prism:endingPage>12</prism:endingPage>
<prism:doi>10.12691/ijpdea-9-1-2</prism:doi>
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