TY - JOUR
T1 - Constructing Solutions to Multi-Term Cauchy–Euler Equations with Arbitrary Fractional Derivatives
AU - Dubovski, Pavel B.
AU - Slepoi, Jeffrey A.
N1 - Publisher Copyright:
© 2024 by the authors.
PY - 2024/7
Y1 - 2024/7
N2 - We further extend the results of other researchers on existence theory to homogeneous fractional Cauchy–Euler equations (Formula presented.) with the derivatives in Caputo or Riemann–Liouville sense. Unlike the existing works, we consider multi-term equations without any restrictions on the order of fractional derivatives. The results are based on the characteristic equations which generate the solutions. Depending on the roots of the characteristic equations (real, multiple, or complex), we construct the corresponding solutions and prove their linear independence.
AB - We further extend the results of other researchers on existence theory to homogeneous fractional Cauchy–Euler equations (Formula presented.) with the derivatives in Caputo or Riemann–Liouville sense. Unlike the existing works, we consider multi-term equations without any restrictions on the order of fractional derivatives. The results are based on the characteristic equations which generate the solutions. Depending on the roots of the characteristic equations (real, multiple, or complex), we construct the corresponding solutions and prove their linear independence.
KW - characteristic equation
KW - fractional Cauchy–Euler equation
KW - fractional derivative
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U2 - 10.3390/math12131928
DO - 10.3390/math12131928
M3 - Article
AN - SCOPUS:85198453364
VL - 12
JO - Mathematics
JF - Mathematics
IS - 13
M1 - 1928
ER -