Solvability of a fractional boundary value problem with fractional derivative condition

A. Guezane-Lakoud, S. Bensebaa
2014 Arabian Journal of Mathematics  
In this paper, we investigate a boundary value problem for fractional differential equations with fractional derivative condition. Some new existence results are obtained using Banach contraction principle and Leray-Schauder nonlinear alternative. Mathematics Subject Classification Introduction Differential equations of fractional order have recently been addressed by many researchers of various fields of science and engineering such as physics, chemistry, biology, economics, control theory,
more » ... control theory, and biophysics. On the other hand, fractional differential equations also serve as an excellent tool for the description of memory and hereditary properties of various materials and processes. With these advantages, the models of fractional order become more and more practical and realistic than the classical models of integer order, such effects in the latter are not taken into account. As a result, the subject of fractional differential equations is gaining much attention and importance. For more details on this theory and on its applications, we refer to the recent monographs of Kilbas et al. [13], Oldham [17], Hilfer [11] and the researches of Engheta [5]. The existence of solutions to fractional boundary value problems is under strong research, see [10, 19, 21] and references therein. More recently, some papers have considered nonlocal boundary value problems for fractional differential equations, in particular Benchohra et al. [3] discussed the existence and uniqueness of solutions for the boundary value problems for differential equations with fractional order and nonlocal conditions of the form
doi:10.1007/s40065-013-0090-1 fatcat:5iskniezjjc7njxd3fiwjoxllq