Operator-Based Approach for the Construction of Solutions to ( C D (1/ n ) ) k -Type Fractional-Order Differential Equations

Inga Telksniene, Zenonas Navickas, Romas Marcinkevičius, Tadas Telksnys (), Raimondas Čiegis and Minvydas Ragulskis
Additional contact information
Inga Telksniene: Mathematical Modelling Department, Faculty of Fundamental Sciences, Vilnius Gediminas Technical University, Saulėtekio al. 11, LT-10223 Vilnius, Lithuania
Zenonas Navickas: Department of Mathematical Modelling, Kaunas University of Technology, Studentu 50-147, LT-51368 Kaunas, Lithuania
Romas Marcinkevičius: Department of Software Engineering, Kaunas University of Technology, Studentu 50-415, LT-51368 Kaunas, Lithuania
Tadas Telksnys: Department of Mathematical Modelling, Kaunas University of Technology, Studentu 50-147, LT-51368 Kaunas, Lithuania
Raimondas Čiegis: Mathematical Modelling Department, Faculty of Fundamental Sciences, Vilnius Gediminas Technical University, Saulėtekio al. 11, LT-10223 Vilnius, Lithuania
Minvydas Ragulskis: Department of Mathematical Modelling, Kaunas University of Technology, Studentu 50-147, LT-51368 Kaunas, Lithuania

Mathematics, 2025, vol. 13, issue 7, 1-20

Abstract: A novel methodology for solving Caputo D ( 1 / n ) C k -type fractional differential equations (FDEs), where the fractional differentiation order is k / n , is proposed. This approach uniquely utilizes fractional power series expansions to transform the original FDE into a higher-order FDE of type D ( 1 / n ) C k n . Significantly, this perfect FDE is then reduced to a k -th-order ordinary differential equation (ODE) of a special form, thereby allowing the problem to be addressed using established ODE techniques rather than direct fractional calculus methods. The effectiveness and applicability of this framework are demonstrated by its application to the fractional Riccati-type differential equation.

Keywords: fractional differential equation; operator calculus; fractional power series expansion (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/7/1169/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/7/1169/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:7:p:1169-:d:1626424

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().