1.Preliminaries 1.1 Some definitions 1.2 Some lemmas 1.3 Some theorems 2.Comparison Principle and Monotone Iterative Method 2.1 Introduction 2.2 Boundary value problem for first order impulsive functional integro-differential equations 2.2.1 Comparison principle 2.2.2 Existence results 2.2.3 Example 2.3 Boundary value problems of nonlinear fractional differential equation with deviating arguments 2.3.1 Preliminaries 2.3.2 Main results 2.3.3 Example 2.4 A class of nonlinear fractional difierential equations 2.4.1 Comparison Theorem and Existence results for dif ferential equation involvingٽL fractional integral operator 2.4.2 Main Results for fractional difierential equation(2.30) 2.4.3 Example 2.5 Explicit iterations and extremal solutions for fractionald ifferential equations with nonlinear integral boundary conditjons 2.5.1 Preliminaries 2.5.2 Existence results 2.5.3 Example 2.6 Explicit iterative solution of a Caputo-Hadamard type frac tional turbulent flow model 2.6.1 Introduction and preliminaries 2.6.2 Comparison principle and explicit solution of linear Caputo-Hadamard type FTFM 2.6.3 Existence results for nonlinear Caputo-Hadamard type FTFM 2.6.4 Example 2.7 Extremal solutions of a nonlinear impulsive differential e quations with multi-orders fractional derivatives 2.7.1 Preliminaries 2.7.2 Main results 2.7.3 Example 2.8 Monotone iterative technique for a nonlinear fractional difference equation of Caputo type 2.8.1 Preliminaries and Comparison Theorem 2.8.2 Existence results for linear and nonlinear fractional -difference equation of Caputo type 2.8.3 Example 2.9 Notes and remarks 3.Monotone Iterative Method and Nonlinear Fractional D ifierential Equation on Finite Interval 3.1 Introduction 3.2 Positive solutions of integral boundary value problem in volving Riemann-Liouville fractional derivative