In the present paper we consider initial value problems for Hilfer fractional differential equations and for system of Hilfer fractional differential equations. By using equivalent integral equations and some fixed point theorems, we study the local existence of solutions. We extend these local existence results globally with the help of continuation theorems and generalized Gronwall inequality.
Bhairat, S. P. (2019). Existence and continuation of solutions of Hilfer fractional differential equations. Journal of Mathematical Modeling, 7(1), 1-20. doi: 10.22124/jmm.2018.9220.1136
MLA
Sandeep P. Bhairat. "Existence and continuation of solutions of Hilfer fractional differential equations". Journal of Mathematical Modeling, 7, 1, 2019, 1-20. doi: 10.22124/jmm.2018.9220.1136
HARVARD
Bhairat, S. P. (2019). 'Existence and continuation of solutions of Hilfer fractional differential equations', Journal of Mathematical Modeling, 7(1), pp. 1-20. doi: 10.22124/jmm.2018.9220.1136
VANCOUVER
Bhairat, S. P. Existence and continuation of solutions of Hilfer fractional differential equations. Journal of Mathematical Modeling, 2019; 7(1): 1-20. doi: 10.22124/jmm.2018.9220.1136
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