TY - JOUR
T1 - Reduction of order formula and fundamental set of solutions for linear fractional differential equations
AU - Al-Refai, Mohammed
N1 - Funding Information:
The author acknowledges the support of the United Arab Emirates University under the Fund No. 31S239-UPAR(1) 2016 .
Publisher Copyright:
© 2018 Elsevier Ltd
PY - 2018/8
Y1 - 2018/8
N2 - In this paper, we consider a class of linear fractional differential equations involving the Caputo–Fabrizio fractional derivative of order 1<α<2. We derive, in closed form, a reduction of order formula to obtain a second linearly independent solution. We then establish a fundamental set of solutions result to the equation. One example is presented to illustrate the validity of the obtained results.
AB - In this paper, we consider a class of linear fractional differential equations involving the Caputo–Fabrizio fractional derivative of order 1<α<2. We derive, in closed form, a reduction of order formula to obtain a second linearly independent solution. We then establish a fundamental set of solutions result to the equation. One example is presented to illustrate the validity of the obtained results.
KW - Caputo–Fabrizio fractional derivative
KW - Fractional differential equations
KW - Fundamental solutions set
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U2 - 10.1016/j.aml.2018.02.014
DO - 10.1016/j.aml.2018.02.014
M3 - Article
AN - SCOPUS:85043282539
SN - 0893-9659
VL - 82
SP - 8
EP - 13
JO - Applied Mathematics Letters
JF - Applied Mathematics Letters
ER -