ON L-FRACTIONAL DERIVATIVES AND L-FRACTIONAL HOMOGENEOUS EQUATIONS

TitleON L-FRACTIONAL DERIVATIVES AND L-FRACTIONAL HOMOGENEOUS EQUATIONS
Publication TypeJournal Article
Year of Publication2017
AuthorsLAZOPOULOS, AK, KARAOULANIS, D
Secondary TitleCommunications in Applied Analysis
Volume21
Issue2
Start Page249
Pagination20
Date Published03/2017
Type of Workscientific: mathematics
ISSN1083-2564
AMS26A33, 34A08, 34K37
Abstract

Many different fractional derivatives exist that serve different aspects of fractional calculus. Nevertheless, they have failed to correspond to a reliable fractional differential. Lazopoulos [22] has introduced the L-fractional derivative having meaningful geometrical configuration. Moreover, the L-fractional derivative has a meaningful fractional differential as well. Hence, Fractional Differential Geometry could be established. The solutions of the linear homogenous L-fractional differential equation with constant coefficients will be studied in the present work. The solutions will be obtained with the help of power series expansions. Numerical solutions are presented for various fractional differentiation orders. Finally, comparison is presented between the cases of fractional differential homogeneous equations with Riemann-Liouville derivatives and Leibnitz derivatives. The similarities and differences are spotted. Those differences support that the solutions of the equations with L-fractional derivatives lie between the conventional (where $\alpha =1$) and the corresponding ones with Riemann-Liouville derivatives.
URLhttp://www.acadsol.eu/en/articles/21/2/6.pdf
DOI10.12732/caa.v21i2.6
Short TitleL-Fractional Derivatives and L-Fractional Equations
Alternate JournalCAA
Refereed DesignationRefereed
Full Text

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