Sequential Riemann–Liouville and Hadamard–Caputo Fractional Differential Equation with Iterated Fractional Integrals Conditions

Sotiris K. Ntouyas, Surang Sitho, Teerasak Khoployklang, Jessada Tariboon
2021 Axioms  
In the present research, we initiate the study of boundary value problems for sequential Riemann–Liouville and Hadamard–Caputo fractional derivatives, supplemented with iterated fractional integral boundary conditions. Firstly, we convert the given nonlinear problem into a fixed point problem by considering a linear variant of the given problem. Once the fixed point operator is available, we use a variety of fixed point theorems to establish results regarding existence and uniqueness. Some
more » ... rties of iteration that will be used in our study are also discussed. Examples illustrating our main results are also constructed. At the end, a brief conclusion is given. Our results are new in the given configuration and enrich the literature on boundary value problems for fractional differential equations.
doi:10.3390/axioms10040277 fatcat:mkws3tqoobdfdc2opryo2dv7qy