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Journal of Applied Nonlinear Dynamics 8(4) (2019) 677--687 | DOI:10.5890/JAND.2019.12.012

K. Balachandran$^{1}$, R. Mabel Lizzy$^{2}$, J. J. Trujillo$^{3}$

$^{1}$ Department of Mathematics, Bharathiar University, Coimbatore 641 046, India

$^{2}$ Chair of Numerical Analysis, Technical University of Munich, 85748 Garching, Germany

$^{3}$ Department de An´alisis Mathem´atico, Universidad de La Laquna, 38271 La Laguna, Tenerife, Spain

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Abstract

In this paper we discuss about the solution representation of abstract fractional differential equations with different conditions on the operator A. The solution representation obtained by using Mittag-Leffler function is correct when the operator A is bounded. However when the operator A is unbounded the representation derived in [1] seems to be incorrect. We also obtain a suitable form of solution to stochastic fractional differential equation with unbounded operators.

Acknowledgments

The first author is thankful to the University Grant Commission for providing a UGC-BSR Faculty Fellowship to carry out this work. The second author is supported by the University Grant Commission under the grant no. MANF-2015-17-TAM-50645 from the Government of India.

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