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Nonlinear fractional differential inclusions with anti-periodic type integral boundary conditions

100%

Ahmad B. , Ntouyas S.

tom 32

nr 1

45-62

This article studies a boundary value problem of nonlinear fractional differential inclusions with anti-periodic type integral boundary conditions. Some existence results are obtained via fixed point theorems. The cases of convex-valued and nonconvex-valued right hand sides are considered. Several new results appear as a special case of the results of this paper.

A study of second order differential inclusions with four-point integral boundary conditions

100%

Ahmad B. , Ntouyas S.

tom 31

nr 2

137-156

In this paper, we discuss the existence of solutions for a four-point integral boundary value problem of second order differential inclusions involving convex and non-convex multivalued maps. The existence results are obtained by applying the nonlinear alternative of Leray Schauder type and some suitable theorems of fixed point theory.

An existence theorem for fractional hybrid differential inclusions of Hadamard type

100%

Ahmad B. , Ntouyas S.

nr 2

207-218

This paper studies the existence of solutions for fractional hybrid differential inclusions of Hadamard type by using a fixed point theorem due to Dhage. The main result is illustrated with the aid of an example.

Existence of solutions for sequential fractional differential equations with four-point nonlocal fractional integral boundary conditions

80%

Ahmad B. , Alsaedi A. , Al-Hutami H.

tom 11

nr 10

1487-1493

This paper investigates the existence of solutions for a nonlinear boundary value problem of sequential fractional differential equations with four-point nonlocal Riemann-Liouville type fractional integral boundary conditions. We apply Banach’s contraction principle and Krasnoselskii’s fixed point theorem to establish the existence of results. Some illustrative examples are also presented.

Existence theory for sequential fractional differential equations with anti-periodic type boundary conditions

80%

Aqlan M. H. , Alsaedi A. , Ahmad B. , Nieto J. J.

Open Mathematics

2016

tom 14

nr 1

723-735

We develop the existence theory for sequential fractional differential equations involving Liouville-Caputo fractional derivative equipped with anti-periodic type (non-separated) and nonlocal integral boundary conditions. Several existence criteria depending on the nonlinearity involved in the problems are presented by means of a variety of tools of the fixed point theory. The applicability of the results is shown with the aid of examples. Our results are not only new in the given configuration but also yield some new special cases for specific choices of parameters involved in the problems.