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Some existence results for a nonlinear fractional differential equation on partially ordered Banach spaces

By using fixed point results on cones, we study the existence and uniqueness of positive solutions for some nonlinear fractional differential equations via given boundary value problems. Examples are presented in order to illustrate the obtained results.

Duality for semi-infinite programming problems involving ( H p , r ) -invex functions

The present paper is framed to study weak, strong and strict converse duality relations for a semi-infinite programming problem and its Wolfe and Mond-Weir-type dual programs under generalized (Hp,r)-invexity.MSC: 90C32, 49K35, 49N15.

Eigenvalues of complementary Lidstone boundary value problems

We consider the following complementary Lidstone boundary value problem ( - 1 ) m y ( 2 m + 1 ) ( t ) = λ F ( t , y ( t ) , y ′ ( t ) ) , t ∈ ( 0 , 1 ) y ( 0 ) = 0 , y ( 2 k - 1 ) ( 0 ) = y ( 2 k - 1 ) ( 1 ) = 0 , 1 ≤ k ≤ m where λ > 0. The values of λ are characterized so that the boundary value problem has a positive solution. Moreover, we derive explicit intervals of λ such...

Oscillation of higher order nonlinear dynamic equations on time scales

Some new criteria for the oscillation of n th order nonlinear dynamic equations of the form x Δ n t + q t x σ ξ t λ = 0 are established in delay ξ(t) ≤ t and non-delay ξ(t) = t cases, where n ≥ 2 is a positive integer, λ is the ratio of positive odd integers. Many of the results are new for the corresponding higher order difference equations and differential equations are as...

Fixed point theory for cyclic generalized contractions in partial metric spaces

Ravi P Agarwal 0 Maryam A Alghamdi Naseer Shahzad nshahzad@kau 0 0 Department of Mathematics, King Abdulaziz University , P.O. Box 80203, Jeddah 21859, Saudi Arabia In this article, we give some

Properties of higher-order half-linear functional differential equations with noncanonical operators

Chenghui Zhang 0 Ravi P Agarwal Martin Bohner Tongxing Li 0 0 School of Control Science and Engineering, Shandong University , Jinan, Shandong 250061 , P.R. China Some new results are presented for

Nonlocal nonlinear integrodifferential equations of fractional orders

In this paper, Schauder fixed point theorem, Gelfand-Shilov principles combined with semigroup theory are used to prove the existence of mild and strong solutions for nonlinear fractional integrodifferential equations of Sobolev type with nonlocal conditions in Banach spaces. To illustrate our abstract results, an example is given. MSC: 35A05, 34G20, 34K05, 26A33.

Study on integro-differential equation with generalized p-Laplacian operator

We tackle the existence and uniqueness of the solution for a kind of integro-differential equations involving the generalized p-Laplacian operator with mixed boundary conditions. This is achieved by using some results on the ranges for maximal monotone operators and pseudo-monotone operators. The method used in this paper extends and complements some previous work.MSC: 47H05, 47H09.

Existence of solutions for integro-differential equations of fractional order with nonlocal three-point fractional boundary conditions

In this paper, we study the existence of solutions for Riemann-Liouville type integro-differential equations of fractional order α ∈ ( 2 , 3 ] with nonlocal three-point fractional boundary conditions via Sadovskii’s fixed point theorem for condensing maps. An illustrative example is also presented. MSC:34A08, 34B10, 34B15.

Inequalities for Green's operator applied to the minimizers

In this paper, we prove both the local and global Lφ -norm inequalities for Green's operator applied to minimizers for functionals defined on differential forms in Lφ -averaging domains. Our results are extensions of Lp norm inequalities for Green's operator and can be used to estimate the norms of other operators applied to differential forms. 2000 Mathematics Subject...

New oscillation results for second-order neutral delay dynamic equations

This paper is concerned with oscillatory behavior of a certain class of second-order neutral delay dynamic equations ( r ( t ) [ x ( t ) + p ( t ) x ( τ ( t ) ) ] Δ ) Δ + q ( t ) x ( δ ( t ) ) = 0 , on a time scale T with sup T = ∞ , where 0 ≤ p ( t ) ≤ p 0 < ∞ . Some new results are presented that not only complement and improve those related results in the literature, but also...

Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String

We introduce the wave equation in fractal vibrating string in the framework of the local fractional calculus. Our particular attention is devoted to the technique of the local fractional Fourier series for processing these local fractional differential operators in a way accessible to applied scientists. By applying this technique we derive the local fractional Fourier series...

New oscillation results for second-order neutral delay dynamic equations

This paper is concerned with oscillatory behavior of a certain class of second-order neutral delay dynamic equations ( r ( t ) [ x ( t ) + p ( t ) x ( τ ( t ) ) ] Δ ) Δ + q ( t ) x ( δ ( t ) ) = 0 , on a time scale T with sup T = ∞ , where 0 ≤ p ( t ) ≤ p 0 < ∞ . Some new results are presented that not only complement and improve those related results in the literature, but also...

Existence and dimension of the set of mild solutions to semilinear fractional differential inclusions

This article studies the existence and dimension of the set for mild solutions of semilinear fractional differential inclusions. We recall and prove some new results on multivalued maps to establish our main results. MSC 2010: 34A12; 34A40.

Fixed Point Theorems in Ordered Banach Spaces and Applications to Nonlinear Integral Equations

Received 5 March 2012; Accepted 20 June 2012 Academic Editor: Simeon Reich Copyright © 2012 Ravi P. Agarwal et al. This is an open access article distributed under the Creative Commons Attribution

Fixed Point Theorems in Ordered Banach Spaces and Applications to Nonlinear Integral Equations

Received 5 March 2012; Accepted 20 June 2012 Academic Editor: Simeon Reich Copyright © 2012 Ravi P. Agarwal et al. This is an open access article distributed under the Creative Commons Attribution

Existence of solutions for integro-differential equations of fractional order with nonlocal three-point fractional boundary conditions

In this paper, we study the existence of solutions for Riemann-Liouville type integro-differential equations of fractional order α ∈ ( 2 , 3 ] with nonlocal three-point fractional boundary conditions via Sadovskii’s fixed point theorem for condensing maps. An illustrative example is also presented.MSC: 34A08, 34B10, 34B15.

Oscillation of higher order nonlinear dynamic equations on time scales

Some new criteria for the oscillation of nth order nonlinear dynamic equations of the form x Δ n t + q t x σ ξ t λ = 0 are established in delay ξ(t) ≤ t and non-delay ξ(t) = t cases, where n ≥ 2 is a positive integer, λ is the ratio of positive odd integers. Many of the results are new for the corresponding higher order difference equations and differential equations are as...

On Integral Transforms and Matrix Functions

The Sumudu transform of certain elementary matrix functions is obtained. These transforms are then used to solve the differential equation of a general linear conservative vibration system, a vibrating system with a special type of viscous damping.

Fixed point-type results for a class of extended cyclic self-mappings under three general weak contractive conditions of rational type

Manuel De la Sen Ravi P Agarwal This article discusses three weak -contractive conditions of rational type for a class of 2-cyclic self-mappings defined on the union of two non-empty subsets of a