Abstract
We discuss existence, uniqueness, and Hyers-Ulam stability of solutions for coupled nonlinear fractional order differential equations (FODEs) with boundary conditions. Using generalized metric space, we obtain some relaxed conditions for uniqueness of positive solutions for the mentioned problem by using Perov’s fixed point theorem. Moreover, necessary and sufficient conditions are obtained for existence of at least one solution by Leray-Schauder-type fixed point theorem. Further, we also develop some conditions for Hyers-Ulam stability. To demonstrate our main result, we provide a proper example.
Highlights
In last few decades, fractional order differential equations (FODEs) become area of interest for the researcher because of high quality accuracy and usability in various fields of science and technology
A lot of physical and natural phenomena can be modeled through FODEs which provide better result than integer order differential equations
Numerous applications of FODEs can be studied in various disciplines like chemical technology, viscoelasticity, industrial robotics, mathematical economy, turbulent filtration in porous media, fractals theory, ecology, economics, plasma physics, metallurgy, electromagnetic theory, biology, signal and image processing, control theory, electric technology, chemical reaction design, potential theory, radio physics, aerodynamics, pharmacokinetics, and so on; further details are available in literature [1,2,3,4,5,6,7]
Summary
FODEs become area of interest for the researcher because of high quality accuracy and usability in various fields of science and technology. Systems of FODEs have been considered in large numbers of research articles, because most of physical, biological, and chemical phenomena can be modeled in the form of systems of FODEs. For example, Su [13] studied existence of solutions for coupled system of fractional differential equations with two-point boundary value problems given as. Wang et al [14] investigate existence and uniqueness of positive solutions to a coupled system of Journal of Function Spaces fractional differential equations with three-point boundary conditions. Motivated by the aforementioned contributions of researchers, we discuss the existence and uniqueness of solutions for coupled system of nonlinear FODEs with boundary conditions involving fractional integral and derivative. The whole analysis is demonstrated by providing a proper example
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