Solvability for a Coupled System of Fractional Differential Equations with Integral Boundary Conditions

The fractional calculus, an active branch of mathematical analysis, is as old as the classical calculus which we know today. In recent years, fractional differential equations have been studied by many researchers, ranging from the theoretical aspects of existence and uniqueness to the numerical methods for finding solutions. It is well known that fractional differential equations provide an excellent tool for the description of memory and hereditary properties of various materials and processes. With these advantages, the fractional models become more practical and realistic than the classical integer-order ones, such effects in the latter are not taken into account. As a result, the subject of fractional differential equations is gaining more and more attention and importance. For more details on this branch of differential equations, please refer to the recent monographs of Miller and Ross [18], Kilbas et al. [13], Lakshmikantham [15], Podlubny[19] , Hilfer [9], and the papers of [1-3, 5-7, 11, 16, 17, 27, 28, 30]. Recently, many researchers paid much attention to the coupled system of fractional differential equations due to its applications in different fields, for instance, see [10, 22-26, 29] and references therein. Wang, Ahmad, et al. [23] discussed a coupled