Abstract
This paper deals with theoretical and constructive existence results for solutions of nonlinear fractional differential equations using the method of upper and lower solutions which generate a closed set. The existence of solutions for nonlinear fractional differential equations involving Riemann‐Liouville differential operator in a closed set is obtained by utilizing various types of coupled upper and lower solutions. Furthermore, these results are extended to the finite systems of nonlinear fractional differential equations leading to more general results.
Highlights
Fractional derivative, introduced around the 17th century, was developed almost until the 19th century
McRae studied an important existence result utilizing the method of upper and lower solutions 36, by means of which, monotone iterative and quasilinearization techniques are developed to fractional differential equations 37–40
Some existence theorems have been established for nonlinear fractional-order differential equations relative to coupled upper and lower solutions
Summary
Fractional derivative, introduced around the 17th century, was developed almost until the 19th century. Since the significance of the fractional calculus has been more clearly perceived, many quality researches have been put forward on this branch of mathematical analysis in the literature see 9–11 and the references therein , and many physical phenomena, chemical processes, biological systems, and so forth have described with fractional derivatives In this framework, fractional differential equations have been gaining much interest and attracting the attention of many researchers. McRae studied an important existence result utilizing the method of upper and lower solutions 36 , by means of which, monotone iterative and quasilinearization techniques are developed to fractional differential equations 37–40.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
