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Existence results for nonlocal boundary value problems for fractional differential equations and inclusions with fractional integral boundary conditions

Sotiris K. Ntouyas (2013)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

This paper studies a new class of nonlocal boundary value problems of nonlinear differential equations and inclusions of fractional order with fractional integral boundary conditions. Some new existence results are obtained by using standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also discussed.

Existence results for q-difference inclusions with three-point boundary conditions involving different numbers of q

Sotiris K. Ntouyas, Thanin Sitthiwirattham, Jessada Tariboon (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we study a new class of three-point boundary value problems of nonlinear second-order q-difference inclusions. Our problems contain different numbers of q in derivatives and integrals. By using fixed point theorems, some new existence results are obtained in the cases when the right-hand side has convex as well as noncovex values.

Existence results for systems of conformable fractional differential equations

Bouharket Bendouma, Alberto Cabada, Ahmed Hammoudi (2019)

Archivum Mathematicum

In this article, we study the existence of solutions to systems of conformable fractional differential equations with periodic boundary value or initial value conditions. where the right member of the system is L α 1 -carathéodory function. We employ the method of solution-tube and Schauder’s fixed-point theorem.

Existence results for systems with nonlinear coupled nonlocal initial conditions

Octavia Bolojan, Gennaro Infante, Radu Precup (2015)

Mathematica Bohemica

The purpose of the present paper is to study the existence of solutions to initial value problems for nonlinear first order differential systems subject to nonlinear nonlocal initial conditions of functional type. The approach uses vector-valued metrics and matrices convergent to zero. Two existence results are given by means of Schauder and Leray-Schauder fixed point principles and the existence and uniqueness of the solution is obtained via a fixed point theorem due to Perov. Two examples are...

Existence results for ϕ-Laplacian Dirichlet BVP of differential inclusions with application to control theory

Smaïl Djebali, Abdelghani Ouahab (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we study ϕ-Laplacian problems for differential inclusions with Dirichlet boundary conditions. We prove the existence of solutions under both convexity and nonconvexity conditions on the multi-valued right-hand side. The nonlinearity satisfies either a Nagumo-type growth condition or an integrably boundedness one. The proofs rely on the Bonhnenblust-Karlin fixed point theorem and the Bressan-Colombo selection theorem respectively. Two applications to a problem from control theory are...

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