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Periodic solutions for third order ordinary differential equations

Juan J. Nieto — 1991

Commentationes Mathematicae Universitatis Carolinae

In this paper, we introduce the concept of upper and lower solutions for third order periodic boundary value problems. We show that the monotone iterative technique is valid and obtain the extremal solutions as limits of monotone sequences. We first present a new maximum principle for ordinary differential inequalities of third order that is interesting by itself.

Some fractional integral formulas for the Mittag-Leffler type function with four parameters

Praveen AgarwalJuan J. Nieto — 2015

Open Mathematics

In this paper we present some results from the theory of fractional integration operators (of Marichev- Saigo-Maeda type) involving the Mittag-Leffler type function with four parameters ζ , γ, Eμ, ν[z] which has been recently introduced by Garg et al. Some interesting special cases are given to fractional integration operators involving some Special functions.

Applications of contractive-like mapping principles to fuzzy equations

Juan J. NietoRosana Rodríguez López — 2006

Revista Matemática Complutense

We recall a recent extension of the classical Banach fixed point theorem to partially ordered sets and justify its applicability to the study of the existence and uniqueness of solution for fuzzy and fuzzy differential equations. To this purpose, we analyze the validity of some properties relative to sequences of fuzzy sets and fuzzy functions.

The monotone iterative technique for periodic boundary value problems of second order impulsive differential equations

Eduardo LizJuan J. Nieto — 1993

Commentationes Mathematicae Universitatis Carolinae

In this paper, we develop monotone iterative technique to obtain the extremal solutions of a second order periodic boundary value problem (PBVP) with impulsive effects. We present a maximum principle for ``impulsive functions'' and then we use it to develop the monotone iterative method. Finally, we consider the monotone iterates as orbits of a (discrete) dynamical system.

Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions

Ming-Xing WangAlberto CabadaJuan J. Nieto — 1993

Annales Polonici Mathematici

The purpose of this paper is to study the periodic boundary value problem -u''(t) = f(t,u(t),u'(t)), u(0) = u(2π), u'(0) = u'(2π) when f satisfies the Carathéodory conditions. We show that a generalized upper and lower solution method is still valid, and develop a monotone iterative technique for finding minimal and maximal solutions.

Extended Riemann-Liouville type fractional derivative operator with applications

P. AgarwalJuan J. NietoM.-J. Luo — 2017

Open Mathematics

The main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind. Some typical generating relations for these extended hypergeometric functions are obtained by defining the extension of the Riemann-Liouville fractional derivative operator. Their connections with elementary functions and Fox’s H-function are also presented.

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

Mohammed H. AqlanAhmed AlsaediBashir AhmadJuan J. Nieto — 2016

Open Mathematics

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...

Nonlinear Implicit Hadamard’s Fractional Differential Equationswith Delay in Banach Space

Mouffak BenchohraSoufyane BouriahJamal E. LazregJuan J. Nieto — 2016

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper, we establish sufficient conditions for the existence of solutions for nonlinear Hadamard-type implicit fractional differential equations with finite delay. The proof of the main results is based on the measure of noncompactness and the Darbo’s and Mönch’s fixed point theorems. An example is included to show the applicability of our results.

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