SPECIAL ISSUE PAPER
Monotone iterative techniques together with Hyers-Ulam-Rassias stability
Kamal Shah,
Liaqat Shah,
Saeed Ahmad,
John Michael Rassias,
Yongjin Li,
Kamal Shah
Department of Mathematics, University of Malakand, Chakdara Dir(L), Pakistan
Search for more papers by this authorLiaqat Shah
Department of Mathematics, University of Malakand, Chakdara Dir(L), Pakistan
Search for more papers by this authorSaeed Ahmad
Department of Mathematics, University of Malakand, Chakdara Dir(L), Pakistan
Search for more papers by this authorJohn Michael Rassias
Pedagogical Department—Mathematics and Informatics, The National and Kapodistrian Universty of Athens, Athens, Greece
Search for more papers by this authorCorresponding Author
Yongjin Li
Department of Mathematics, Sun Yat-Sen University, Guangzhou, China
Correspondence
Yongjin Li, Department of Mathematics, Sun Yat-Sen University, Guangzhou, China.
Email: [email protected]
Communicated by: D. Zeidan
Search for more papers by this authorKamal Shah,
Liaqat Shah,
Saeed Ahmad,
John Michael Rassias,
Yongjin Li,
Kamal Shah
Department of Mathematics, University of Malakand, Chakdara Dir(L), Pakistan
Search for more papers by this authorLiaqat Shah
Department of Mathematics, University of Malakand, Chakdara Dir(L), Pakistan
Search for more papers by this authorSaeed Ahmad
Department of Mathematics, University of Malakand, Chakdara Dir(L), Pakistan
Search for more papers by this authorJohn Michael Rassias
Pedagogical Department—Mathematics and Informatics, The National and Kapodistrian Universty of Athens, Athens, Greece
Search for more papers by this authorCorresponding Author
Yongjin Li
Department of Mathematics, Sun Yat-Sen University, Guangzhou, China
Correspondence
Yongjin Li, Department of Mathematics, Sun Yat-Sen University, Guangzhou, China.
Email: [email protected]
Communicated by: D. Zeidan
Search for more papers by this authorAbstract
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.
CONFLICT OF INTEREST
All authors declare that there is no conflict of interest.
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