Received: 25 July 2018 DOI: 10.1002/mma.5407 RESEARCH ARTICLE On stable iterative solutions for a class of boundary value problem of nonlinear fractional order differential equations Sajjad Ali 1 Kamal Shah 2 Fahd Jarad 3 1 Department of Mathematics, Shaheed Benazir Bhutto University Sheringal, Dir Upper, Khyber Pakhtunkhwa, Pakistan 2 Department of Mathematics, University of Malakand, Dir Lower, Khyber Pakhtunkhwa, Pakistan 3 Department of Mathematics, Çankaya University, Ankara, Turkey Correspondence Fahd Jarad, Department of Mathematics, Çankaya University, Ankara 06790, Turkey. Email: fahd@cankaya.edu.tr Communicated by: D. Zeidan MSC Classification: 26A33; 34A08; 35B40 In this article, sufficient conditions for the existence of extremal solutions to nonlinear boundary value problem (BVP) of fractional order differential equations (FDEs) are provided. By using the method of monotone iterative tech- nique together with upper and lower solutions, conditions for the existence and approximation of minimal and maximal solutions to the BVP under considera- tion are constructed. Some adequate results for different kinds of Ulam stability are investigated. Maximum error estimates for the corresponding solutions are given as well. Two examples are provided to illustrate the results. KEYWORDS fractional differential equations, monotone iterative technique, Ulam stability, upper and lower solutions extremal solutions 1 INTRODUCTION In recent times, the area of fractional differential equations (FDEs) has attracted many scientists working in different areas because it turned out that good results are obtained when FDEs are used to model physical phenomena in numerous fields of science and engineering like biology, chemistry, mechanics, economics, polymer, aerodynamics, biophysics, and control theory. 1-8 In this regard, different aspects of FDEs have been investigated in the last few decades like qualitative theory, stability analysis, and numerical solutions. In variety of research work, different authors have done valuable work to search the basic properties and features of fractional derivatives and integrals. In this concern, many researchers studied the exis- tence and uniqueness of solutions to FDEs, see previous studies. 9-17 In last few years, new kinds of fractional derivatives including nonsingular and Mittag-Leffler type kernels have been introduced. Also, some authors have given attention to study conformable fractional order derivatives and their applications, for detail see the studies of Abdeljawad et al. 18-21 The aforesaid results were based on classical fixed point theorems and nonlinear functional analysis. As far, we know the aforesaid area has been greatly developed. On the other hand, iterative techniques have been considered in many articles, see previous studies. 22-25 The monotone iterative technique together with the method of upper and lower solutions are important tools for providing the existence and approximation of solutions to many applied problems of differential and integral equations. 26-36 The aforesaid scheme has been considered by few authors for FDEs. For instance, Khan 37 developed the aforesaid scheme for the following class of FDEs { D p w(t)+ K(t, w(t)) = 0, t ∈(0, 1), 1 < p < 2, w ′ (t)| t=0 = 0, w(1)= x( ), Math Meth Appl Sci. 2018;1–13. wileyonlinelibrary.com/journal/mma © 2018 John Wiley & Sons, Ltd. 1