Further studies on ordinary differential equations involving the $ M $-fractional derivative-Reference-Cited by-同舟云学术

Further studies on ordinary differential equations involving the $ M $-fractional derivative

Published:2022 Issue:6 Volume:7 Page:10977-10993
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Khoshkenar A.¹,Ilie M.¹,Hosseini K.¹²,Baleanu D.³⁴⁵,Salahshour S.⁶,Park C.⁷,Lee J. R.⁸

Affiliation:

1. Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran

2. Department of Mathematics, Near East University TRNC, Mersin 10, Turkey

3. Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Ankara 06530, Turkey

4. Institute of Space Sciences, Magurele-Bucharest, Romania

5. Department of Medical Research, China Medical University, Taichung, 40447, Taiwan

6. Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey

7. Research Institute for Natural Sciences, Hanyang University, Seoul 04763, South Korea

8. Department of Data Science, Daejin University, Kyunggi 11159, South Korea

Abstract

<abstract><p>In the current paper, the power series based on the $ M $-fractional derivative is formally introduced. More peciesely, the Taylor and Maclaurin expansions are generalized for fractional-order differentiable functions in accordance with the $ M $-fractional derivative. Some new definitions, theorems, and corollaries regarding the power series in the $ M $ sense are presented and formally proved. Several ordinary differential equations (ODEs) involving the $ M $-fractional derivative are solved to examine the validity of the results presented in the current study.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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