Abstract
This paper is concerned with the existence and uniqueness of solutions for a coupled system of fractional differential equations supplemented with the multi-strip and multi-point mixed boundary conditions. The existence of solutions is derived by applying Leray-Schauder’s alternative, while the uniqueness of the solution is established via Banach’s contraction principle. We also show the existence and uniqueness results of a positive solution by applying the Krasnoselskii fixed point theorem.
Highlights
1 Introduction Fractional differential equations arise from the studies of complex problems in many engineering and scientific as the mathematical modeling of systems and processes in the fields of physics, chemistry, biology, economics, control theory, signal and image processing, biophysics, blood flow phenomena, aerodynamics, fitting of experimental data
Fractional order boundary value problems, fractional evolution equations, impulsive fractional differential equations, fractional partial differential equations are found to be of significant interest for many researchers [ – ]
By applying Leray-Schauder’s alternative, Banach’s contraction principle and the fixed point theorems of cone expansion and compression of norm type, the sufficient conditions for the existence and uniqueness results to a general class of multi-strip and multi-point mixed boundary value problem for a coupled system of fractional differential equations are obtained
Summary
Fractional differential equations arise from the studies of complex problems in many engineering and scientific as the mathematical modeling of systems and processes in the fields of physics, chemistry, biology, economics, control theory, signal and image processing, biophysics, blood flow phenomena, aerodynamics, fitting of experimental data. By applying Leray-Schauder’s alternative, Banach’s contraction principle and the fixed point theorems of cone expansion and compression of norm type, the sufficient conditions for the existence and uniqueness results to a general class of multi-strip and multi-point mixed boundary value problem for a coupled system of fractional differential equations are obtained. We prove existence and uniqueness of solutions of the boundary value problem ) are the multistrip and multi-point mixed boundary conditions, the existence and uniqueness conclusions could be obtained by using the definition of the Caputo type fractional q-derivative.
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