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Extremal solutions to a coupled system of nonlinear fractional differential equations with ψ–Caputo fractional derivatives

Derbazi Choukri, Baitiche Zidane, Benchohra Mouffak, Graef John R.

Journal of Mathematics and Applications

2021

Vol. 44

19--34

Using the well-known monotone iterative technique together with the method of upper and lower solutions, the authors investigate the existence of extremal solutions to a class of coupled systems of nonlinear fractional differential equations involving the ψ–Caputo derivative with initial conditions. As applications of this work, two illustrative examples are presented.

Monotone iterative technique for non-autonomous semilinear differentia equations with nonlocal condition

Meraj Arshi, Pandey Dwijendra Narain

Demonstratio Mathematica

2019

Vol. 52, nr 1

29--39

The objective of this article is to discuss the existence and uniqueness of mild solutions for a class of non-autonomous semilinear differential equations with nonlocal condition via monotone iterative method with upper and lower solutions in an ordered complete norm space X, using evolution system and measure of noncompactness.