<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">A.K. LAZOPOULOS</style></author><author><style face="normal" font="default" size="100%">D. KARAOULANIS</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON L-FRACTIONAL DERIVATIVES AND L-FRACTIONAL HOMOGENEOUS EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Communications in Applied Analysis</style></secondary-title><alt-title><style face="normal" font="default" size="100%">CAA</style></alt-title><short-title><style face="normal" font="default" size="100%">L-Fractional Derivatives and L-Fractional Equations</style></short-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A33</style></keyword><keyword><style  face="normal" font="default" size="100%">34A08</style></keyword><keyword><style  face="normal" font="default" size="100%">34K37</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">03/2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/21/2/6.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">21</style></volume><pages><style face="normal" font="default" size="100%">20</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;Many different fractional derivatives exist that serve&amp;nbsp;different aspects of fractional calculus. Nevertheless, they have&amp;nbsp;failed to correspond to a reliable fractional differential. Lazopoulos [22]&amp;nbsp;has introduced the L-fractional derivative having meaningful geometrical&amp;nbsp;configuration. Moreover, the L-fractional derivative has a meaningful&amp;nbsp;fractional differential as well. Hence, Fractional Differential Geometry&amp;nbsp;could be established. The solutions of the linear homogenous L-fractional&amp;nbsp;differential equation with constant coefficients will be studied in the&amp;nbsp;present work. The solutions will be obtained with the help of power series&amp;nbsp;expansions. Numerical solutions are presented for various fractional&amp;nbsp;differentiation orders. Finally, comparison is presented between the cases&amp;nbsp;of fractional differential homogeneous equations with Riemann-Liouville&amp;nbsp;derivatives and Leibnitz derivatives. The similarities and differences are&amp;nbsp;spotted. Those differences support that the solutions of the equations with&amp;nbsp;L-fractional derivatives lie between the conventional (where $\alpha =1$) and the corresponding ones with Riemann-Liouville derivatives.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><work-type><style face="normal" font="default" size="100%">scientific: mathematics</style></work-type><section><style face="normal" font="default" size="100%">249</style></section></record></records></xml>