Open AccessNonlocal initial value problems for implicit differential equations with Hilfer–Hadamard fractional derivative
Author(s) -
D. Vivek,
K. Kanagarajan,
E. M. Elsayed
Publication year - 2018
Publication title -
nonlinear analysis
Language(s) - English
Resource type - Journals
eISSN - 2335-8963
pISSN - 1392-5113
DOI - 10.15388/na.2018.3.4
Subject(s) - hadamard transform , mathematics , fixed point theorem , fractional calculus , contraction principle , derivative (finance) , mathematical analysis , banach space , generalizations of the derivative , stability (learning theory) , contraction (grammar) , fixed point , differential (mechanical device) , differential equation , initial value problem , contraction mapping , value (mathematics) , pure mathematics , physics , computer science , economics , statistics , financial economics , thermodynamics , medicine , machine learning
Fractional differential equations (FDEs) have been applied in many fields such as physics, mechanics, chemistry, engineering etc. There has been a significant development in ordinary differential equations involving fractional-order derivatives, one can see the monographs of Hilfer [19], Kilbas [16] and Podlubny [18] and the references therein. Moreover, Hilfer [19] studied applications of a generalized fractional operator having the Riemann– Liouville and the Caputo derivatives as specific cases. Hilfer fractional derivative has been receiving more and more attention in recent times; see, for example, [8–11, 14, 21, 24]. Benchohra et al. [4, 5] studied implicit differential equations(IDEs) of fractional order in various aspects. Recently, some mathematicians have considered FDEs depending on the Hadamard fractional derivative [2, 6, 7].