ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

On Representation of Solutions of Abstract Fractional Differential Equations

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

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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