Fractional Differential Equations and Expansions in Fractional Powers-Reference-Cited by-同舟云学术

Fractional Differential Equations and Expansions in Fractional Powers

Published:2023-09-29 Issue:10 Volume:15 Page:1842
ISSN:2073-8994
Container-title:Symmetry
language:en
Short-container-title:Symmetry

Author:

Caratelli Diego¹²,Natalini Pierpaolo³,Ricci Paolo Emilio⁴^ORCID

Affiliation:

1. The Antenna Company, High Tech Campus 29, 5656 AE Eindhoven, The Netherlands

2. Department of Electrical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

3. Department of Mathematics and Physics, Roma Tre University, Largo San Leonardo Murialdo 1, 00146 Rome, Italy

4. Mathematics Section, International Telematic University UniNettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, Italy

Abstract

We use power series with rational exponents to find exact solutions to initial value problems for fractional differential equations. Certain problems that have been previously studied in the literature can be solved in a closed form, and approximate solutions are derived by constructing recursions for the relevant expansion coefficients.

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2073-8994/15/10/1842/pdf

Reference20 articles.

1. Samko, S., Kilbas, A.A., and Marichev, O. (1993). Fractional Integrals and Derivatives, Taylor & Francis.

2. Carpinteri, A., and Mainardi, F. (1997). Fractals and Fractional Calculus in Continuum Mechanics, Springer.

3. The fundamental solution of the space-time fractional diffusion equation;Mainardi;Fract. Calc. Appl. Anal.,2001

4. Abd-Elhameed, W.M., and Alsuyuti, M.M. (2023). Numerical Treatment of Multi-Term Fractional Differential Equations Via a New Kind of Generalized Chebyshev Polynomials. Fractal Fract., 7.

5. Systems-based decomposition schemes for the approximate solution of multi-term fractional differential equations;Ford;J. Comput. Appl. Math.,2009

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