%0 Journal Article %T Investigating a Coupled System with Riemann-Liouville Fractional Derivative by Modified Monotone Iterative Technique %J Communications in Nonlinear Analysis %I Research & Science Group Ltd. %Z 2371-7920 %A Shah, Kamal %A Hussain, Abid %D 2023 %\ 07/01/2023 %V 11 %N 2 %P 1-18 %! Investigating a Coupled System with Riemann-Liouville Fractional Derivative by Modified Monotone Iterative Technique %K Arbitrary order differential equations %K Monotone iterative technique %K Riemann-Liouville fractional derivative %K Perov’s and Schuader’s fixed point theorems %R %X In recent time, the area of arbitrary order differential equations (AODEs)has been considered very well. Different aspects have been investigated for the saidarea. One of the important and most warm area is devoted to study multiplicityresults along with existence and uniqueness of solutions for the said equations. In thisregard various techniques have been utilized to investigate the said area. Monotoneiterative technique (MIT) coupled with the method of extremal solutions has beenused recently to investigate multiplicity of solutions to some AODEs. In this researchwork, we deal a coupled system of nonlinear AODEs under boundary conditions (BCs)involving Riemann-Liouville fractional derivative by using fixed point theorems dueto Perov’s and Schuader’s to study existence and uniqueness results. Using Perove’sfixed point theorem ensures uniqueness of solution to systems of equations, whileexistence of at least one solution is achieved by Schauder’s fixed point theorem.Then we come across the multiplicity of solutions and establish some criteria for theiterative solutions via using updated type MIT together with the method of upper andlower solutions for the considered system of AODEs. Corresponding to multiplicityresults of solutions, we first establish two sequences of extremal solutions. One of thesequence is monotonically decreasing and converging to lower solution. On the otherhand, the other sequence is monotonically increasing and converging to the uppersolution. In last we give suitable examples to illustrate the main results. %U https://www.cna-journal.com/article_102672_4525fa4a1423a8a43736dd3b67f066ab.pdf