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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.

Multiple solutions of boundary value problems on time scales for φ-laplacian operator

Amster Pablo, Kuna Mariel Paula, Santos Dionicio Pastor

Opuscula Mathematica

2020

Vol. 40, no. 4

405--425

We establish the existence and multiplicity of solutions for some boundary value problems on time scales with a y-Laplacian operator. For this purpose, we employ the concept of lower and upper solutions and the Leray-Schauder degree. The results extend and improve known results for analogous problems with discrete p-Laplacian as well as those for boundary value problems on time scales.

Positive solution of a fractional differential equation with integral boundary conditions

Abdo M. S., Wahash H. A., Panchal S. K.

Journal of Applied Mathematics and Computational Mechanics

2018

Vol. 17, nr 3

5--15

In this paper, we prove the existence and uniqueness of a positive solution for a boundary value problem of nonlinear fractional differential equations involving a Caputo fractional operator with integral boundary conditions. The technique used to prove our results depends on the upper and lower solution, the Schauder fixed point theorem and the Banach contraction principle. The result of existence obtained through constructing the upper and lower control functions of the nonlinear term without any monotone requirement.

Impulsive functional-differential equations of first order

Skóra L.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2007

Vol. 47, [Z] 2

207-219

In this paper we present some existence results for impulsive functionaldifferential equations of first order.

A generalized upper and lower solution method for singular discrete boundary value problems for the one-dimensional p-Laplacian

Jiang D. Q., O'Regan D., Agarwal R. P.

Journal of Applied Analysis

2005

Vol. 11, nr 1

35-47

This paper presents new existence results for singular discrete boundary value problems for the one-dimension p-Laplacian. In particular our nonlinearity may be singular in its dependent variable and is allowed to change sign. Our results are new even for p = 2