TY - JOUR
T1 - Hilfer-type fractional differential equations with variable coefficients
AU - Restrepo, Joel E.
AU - Suragan, Durvudkhan
N1 - Funding Information:
The authors were supported by the Nazarbayev University Program 091019CRP2120. Joel E. Restrepo thanks to Colciencias and Universidad de Antioquia (Convocatoria 848-Programa de estancias postdoctorales 2019) for their support. This research was funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP09058317) and Grant “Dynamical Analysis and Synchronization of Complex Neural Networks with Its Applications”.
Publisher Copyright:
© 2021 Elsevier Ltd
PY - 2021/9
Y1 - 2021/9
N2 - In this paper, we give a representation of the solution of Hilfer-type fractional differential equations with continuous variable coefficients. The solution is represented by convergent infinite series involving composition of Riemann–Liouville fractional integral operators. The obtained representation of the solution can be used effectively for computational and analytic purposes. For the case of constant coefficients, the solution is given by the Riemann-Liouville fractional integral of the multivariate Mittag-Leffler function.
AB - In this paper, we give a representation of the solution of Hilfer-type fractional differential equations with continuous variable coefficients. The solution is represented by convergent infinite series involving composition of Riemann–Liouville fractional integral operators. The obtained representation of the solution can be used effectively for computational and analytic purposes. For the case of constant coefficients, the solution is given by the Riemann-Liouville fractional integral of the multivariate Mittag-Leffler function.
KW - Hilfer fractional derivative
KW - Linear fractional differential equation
KW - Mittag-Leffler function
KW - Variable coefficient
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U2 - 10.1016/j.chaos.2021.111146
DO - 10.1016/j.chaos.2021.111146
M3 - Article
AN - SCOPUS:85111036946
SN - 0960-0779
VL - 150
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
M1 - 111146
ER -