Premium
Monotone iterative techniques together with Hyers‐Ulam‐Rassias stability
Author(s) -
Shah Kamal,
Shah Liaqat,
Ahmad Saeed,
Rassias John Michael,
Li Yongjin
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5825
Subject(s) - mathematics , monotone polygon , monotonic function , upper and lower bounds , nonlinear system , iterative method , stability (learning theory) , fractional calculus , boundary value problem , derivative (finance) , mathematical analysis , mathematical optimization , physics , geometry , quantum mechanics , machine learning , computer science , financial economics , economics
In this article, the first purpose is treating a coupled system of nonlinear boundary value problems (BVPs) of fractional‐order differential equations (FODEs) for existence of solutions. The corresponding fractional‐order derivative is taken in Riemann‐Liouville sense. The require results for iterative solutions are obtained by using monotone iterative techniques combine with the method of upper and lower solutions. In this regard, two sequences are established for upper and lower solutions, respectively, in which one is monotonically increasing and converges to upper solution, while other one is monotonically decreasing converges to lower solution of the considered problem. The second purpose is discussing different kinds Ulam stability results for the proposed problem. Some applications of our results are also provided.