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Existence of solutions for fractional differential inclusions with nonlocal Riemann-Liouville integral boundary conditions

Bashir Ahmad;  Sotiris Ntouyas — 2014

Mathematica Bohemica

In this paper, we discuss the existence of solutions for a boundary value problem of fractional differential inclusions with nonlocal Riemann-Liouville integral boundary conditions. Our results include the cases when the multivalued map involved in the problem is (i) convex valued, (ii) lower semicontinuous with nonempty closed and decomposable values and (iii) nonconvex valued. In case (i) we apply a nonlinear alternative of Leray-Schauder type, in the second case we combine the nonlinear alternative...

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.

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

Bashir Ahmad;  Sotiris K. Ntouyas — 2012

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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

Bashir Ahmad;  Sotiris K. Ntouyas — 2011

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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.

Oscillation of impulsive conformable fractional differential equations

Jessada Tariboon;  Sotiris K. Ntouyas — 2016

Open Mathematics

In this paper, we investigate oscillation results for the solutions of impulsive conformable fractional differential equations of the form tkDαpttkDαxt+rtxt+qtxt=0,t≥t0,t≠tk,xtk+=akx(tk−),tkDαxtk+=bktk−1Dαx(tk−),k=1,2,…. t k D α p t t k D α x t + r t x t + q t x t = 0 , t ≥ t 0 , t ≠ t k , x t k + = a k x ( t k - ) , t k D α x t k + = b k t k - 1 D α x ( t k - ) , k = 1 , 2 , ... . Some new oscillation results are obtained by using the equivalence transformation and the associated Riccati techniques.

Existence of mild solutions on semiinfinite interval for first order differential equation with nonlocal condition

Mouffak Benchohra;  Sotiris K. Ntouyas — 2000

Commentationes Mathematicae Universitatis Carolinae

In this paper we investigate the existence of mild solutions defined on a semiinfinite interval for initial value problems for a differential equation with a nonlocal condition. The results is based on the Schauder-Tychonoff fixed point theorem and rely on a priori bounds on solutions.

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