non self adjoint zakharov shabat operator with a potential of the finite asymptotic values i direct spectral and scattering problems the zakharov and shabat equation for the scattering problem is studied the estimates analytical properties and asymptotic expansions of the jost solution are presented for a general class of the potentials q x not vanishing at infinity the existence of the similarity transformation is also shown for q x vanishing at infinity the continuous part of the spectrum doubly degenerates however nonvanishing finite asymptotic values of q x dissolve the degeneracy completely the expansion theorem is given in c 0 2 r and for a class of q x we prove that the zakharov and shabat equation yields a non self adjoint spectral operator in the hilbert space in the sense of dunford and schwartz

a numerical algorithm for a class of fractional bvps with p laplacian operator and singularity the convergence and dependence analysis abstract in the paper we establish the uniqueness of positive solutions for a model of higher order singular fractional boundary value problems with p laplacian operator the equation includes the caputo and the riemann liouville fractional derivative the boundary conditions contain riemann stieltjes integrals and nonlocal infinite point boundary conditions the nonlinear terms f and h may be singular on the time variable and space variables the uniqueness result is obtained by the theory of mixed monotone operators we also discuss the dependence of solutions upon a parameter furthermore two examples illustrate our main results via numerical analysis

the zakharov shabat inverse spectral problem for operators many soliton equations their solutions and their properties can be deduced from simpler essentially linear equations involving more complicated objects e g integral operators the deduction process from the operator valued equation to the scalar one amounts to some rather simple procedure like taking a trace or a determinant this is described for the class of soliton equations solvable with the zakharov shabat spectral transform

new bounds for the first inequality of ostrowski gruss type and applications abstract some new bounds for the first inequality of ostrowski gruss type are derived these new bounds can be much better than some recently obtained bounds applications in numerical integration are also given

error bounds in approximating the riemann stieltjes integral of c n 1 class integrands and nonsmooth integrators in the present paper we investigate the problem of approximating the riemann stieltjes integral a b f du in the case when the integrand f is n 1 time differentiable n 0 and the derivative f n 1 is continuous on a b while the integrator u is riemann integrable on a b a priory error bounds for different classes of functions are provided

on an inequality of ostrowski type in three independent variables in the present paper a new inequality of ostrowski type in three independent variables is established the discrete analogue of the main result is also given

exact solutions to the sine gordon equation a systematic method is presented to provide various equivalent solution formulas for exact solutions to the sine gordon equation such solutions are analytic in the spatial variable x and the temporal variable t and they are exponentially asymptotic to integer multiples of 2 as x the solution formulas are expressed explicitly in terms of a real triplet of constant matrices the method presented is generalizable to other integrable evolution equations where the inverse scattering transform is applied via the use of a marchenko integral equation by expressing the kernel of that marchenko equation using a matrix exponential in terms of the matrix triplet and by exploiting the separability of that kernel an exact solution formula to the marchenko equation is derived yielding various equivalent exact solution formulas for the sine gordon equation

symmetric positive solutions to singular system with multi point coupled boundary conditions in this paper we study the existence and multiplicity of symmetric positive solutions for a nonlinear system with multi point coupled boundary conditions the arguments are based upon a specially constructed cone and the fixed point index theorem in cones an example is then given to demonstrate the applicability of our results

three point rules in numerical integration identities and inequalities are obtained involving evaluations at an interior and at the end points it is shown how previous work and rules in numerical integration are recaptured as particular instances of the current development explicit a priori bounds are provided allowing the determination of the partition required for achieving a prescribed error tolerance in the main ostrowski gruss type inequalities are used to obtain bounds on the rules in terms of a variety of norms

hadamard type inequalities for s convex functions in this paper we establish some new inequalities for differentiable functions based on concavity and s convexity we also prove several hadamard type inequalities for products of two convex and s convex functions

comparing two integral means for absolutely continuous functions whose absolute value of the derivative are convex and applications abstract some new estimates for the difference between the integral mean of a function and its mean over a subinterval are established and new applications for special means and probability density functions are also given

on the existence of solutions for fractional differential inclusions with sum and integral boundary conditions in this paper by using the endpoint result for multifunctions we investigate the existence of solutions for a boundary value problem for fractional differential inclusions with sum and integral boundary conditions finally an example is also given to illustrate the validity of our main result

a straightforward method for finding implicit solitary wave solutions of nonlinear evolution and wave equations the authors present a straightforward method for finding implicit solutions for nonlinear evolution and wave equations the method is illustrated by finding implicit single solitary wave solutions for the harry dym korteweg de vries modified korteweg de vries boussinesq and the generalised korteweg de vries equations

on sharp inequalities of simpson type and ostrowski type in two independent variables in this paper two sharp inequalities are derived the first is a sharp simpson inequality and the second is a sharp inequality of ostrowski type in two independent variables

on new inequalities of simpson s type for s convex functions in this paper we establish some new inequalities of simpson s type based on s convexity some applications to special means of real numbers are also given

inequalities for h preinvex functions in this paper we introduce the class of h preinvex functions and we prove some new inequalities for differentiable functions based on h preinvexity

on h convexity abstract we introduce a class of h convex functions which generalize convex s convex godunova levin functions and p functions namely the h convex function is defined as a non negative function f j r which satisfies f x 1 y h f x h 1 f y where h is a non negative function 0 1 and x y j some properties of h convex functions are discussed also the schur type inequality is given

some lipschitz type inequalities for complex functions abstract in this paper we establish some lipschitz type inequalities for complex functions when some convexity properties for powers of the absolute value of the derivative are assumed the case of functions defined by power series is analyzed some applications in bounding the jensen difference for complex functions are also provided

stability analysis by krasnoselskii s fixed point theorem for nonlinear fractional differential equations this paper is concerned with the stability analysis of nonlinear fractional differential equations of order 1 2 our main results are obtained by using krasnoselskii s fixed point theorem in a weighted banach space an example and its corresponding simulation are presented to illustrate the main results

inequalities of hadamard s type for lipschitzian mappings and their applications in this paper we give some inequalities of hadamard s type for m lipschitzian functions some applications which are connected with arithmetic mean geometric mean harmonic mean logarithmical mean identric mean etc for two positive numbers are also given

multiplicity of solutions for integral boundary value problems of fractional differential equations with upper and lower solutions abstract in this paper we study the existence of multiple solutions for the integral boundary value problems of fractional differential equations by the method of upper and lower solutions and leray schauder degree theory the sufficient conditions about the existence of at least three solutions are obtained moreover it is proved that the integral boundary value problem has at least three positive solutions under the conditions of m 0 and f is nonnegative by given two upper and lower solutions which can be easily obtained through our methods we can present the existence theorem of at least three solutions two examples are also included to illustrate the effectiveness of the proposed results

new error bounds for the simpson s quadrature rule and applications new error bounds for the well known simpson s quadrature rule are derived if we use these bounds then we can apply the simpson s rule to functions whose first second or third derivatives are unbounded below or above furthermore these error bounds can be much better than some recently obtained bounds applications in numerical integration are also given

two new theorem on mappings uniformly continuous and convex with applications to quadrature rules and means an interesting connection exists between convex functions and uniformly continuous functions this linkage leads to some interesting functional inequalities over the open interval which works well in quadrature rules and means in this paper we establish two new theorem which connect the hermite hadamard type functions

two mappings in connection to hadamard s inequalities w are known in the literature as hadamard s inequalities we note that j hadamard was not the first who discovered them as is pointed out by d s mitrinovic and i b laekovic 3 the inequalities 1 are due to c hermite who obtained them in 1883 ten years before j hadamard in this paper by the use of mappings 2 and 4 we shall establish some refinements of 1 for other inequalities in connection to hadamard s result see 1 2 51 where further references are given

exact solitary wave solutions of nonlinear evolution and wave equations using a direct algebraic method the authors present a systematic and formal approach toward finding solitary wave solutions of nonlinear evolution and wave equations from the real exponential solutions of the underlying linear equations the physical concept is one of the mixing of these elementary solutions through the nonlinearities in the system the emphasis is however on the mathematical aspects i e the formal procedure necessary to find single solitary wave solutions by means of examples it is shown how various cases of pulse type and kink type solutions are to be obtained by this method an exhaustive list of equations so treated is presented in tabular form together with the particular intermediate relations necessary for deriving their solutions the extension of the technique to construct n soliton solutions and indicate connections with other existing methods is outlined

ostrowski s type inequalities for some classes of continuous functions of selfadjoint operators in hilbert spaces new ostrowski s type inequalities for some classes of continuous functions of selfadjoint operators in hilbert spaces under suitable assumptions for the involved operators are given

a new generalization of ostrowski type inequality involving functions of two independent variables the main purpose of this paper is to derive a new inequality of ostrowski type involving functions of two independent variables by using certain integral inequalities

on generalization of different type inequalities for harmonically quasi convex functions via fractional integrals in this paper a new general identity for fractional integrals have been defined by using of this identity new estimates on generalization of hadamard ostrowski and simpson like type inequalities for harmonically quasi convex functions via the riemann liouville fractional integral have been obtained

refinements and similar extensions of hermite hadamard inequality for fractional integrals and their applications in this paper we establish some new refinements and similar extensions of hermite hadamard inequality for fractional integrals and present several applications in the beta function

differences between means with bounds from a riemann stieltjes integral an identity for the difference between two integral means is obtained in terms of a riemann stieltjes integral this enables bounds to be procured when the integrand is of bounded variation lipschitzian and monotonic if f is absolutely continuous bounds are also obtained for f lp a b 1 p the usual lebesgue norms this supplements earlier results involving f l a b

a theorem on mappings with bounded derivatives with applications to quadrature rules and means in this paper we establish a new inequality of theorem 2 appl math lett 13 2000 19 dragomir s integral inequality for functions whose derivatives are bounded this has immediate applications in numerical integration where new estimates are obtained for the remainder term of the trapezoid mid point some natural applications to special means of real numbers are given for several recent results concerning dragomir s integral inequality see appl math lett 13 2000 19 where further references are listed

on some inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula some inequalities are presented here for differentiable convex mappings using hermite hadamard s integral inequality holding for convex functions a parallel development is deduced for differentiable concave functions some applications to special means of real numbers are also given finally some error estimates for the midpoint formula are obtained

hadamard type inequalities for lipschitzian functions in one and two variables with applications abstract in this paper we shall establish some hadamard type inequalities for lipschitzian functions in one and two variables and give several applications for special means

convexity according to a pair of quasi arithmetic means and inequalities abstract we consider a class of generalized convex functions which are defined according to a pair of quasi arithmetic means and called m m convex functions and establish various fejer type inequalities for such a function class these inequalities not merely provide a natural and intrinsic characterization of the m m convex functions but actually offer a generalization and refinement of the most part of the concrete hermite hadamard and fejer type inequalities obtained in earlier studies for different kinds of convexity and fractional integrals applications to inequalities involving the gamma function and special means are also included

existence results for a coupled system of caputo type sequential fractional differential equations with nonlocal integral boundary conditions this paper is concerned with the existence and uniqueness of solutions for a coupled system of caputo type sequential fractional differential equations supplemented with nonlocal riemann liouville integral boundary conditions the existence of solutions is derived by applying leray schauder s alternative while the uniqueness of solution is established via banach s contraction principle an illustrative example is also included the paper concludes with some interesting observations

extensions of the hermite hadamard inequality for harmonically convex functions via fractional integrals the main aim of this paper is to give extensions of the hermite hadamard inequality for harmonically convex functions via riemann liouville fractional integrals we show how to relax the harmonically convexity property of the function f obtained results in this work involve a larger class of functions our results are the refinements of the existing results for harmonically convex functions

inequalities of hadamard s type for lipschitzian mappings in this paper we establish several inequalities of hadamard s type for lipschitzian mappings

some classes of solutions to the toda lattice hierarchy we apply an analogue of the zakharov shabat dressing method to obtain infinite matrix solutions to the toda lattice hierarchy using an operator transformation we convert some of these into solutions in terms of integral operators and fredholm determinants others are converted into a class of operator solutions to the l periodic toda hierarchy

hermite hadamard type inequalities for harmonically convex functions via fractional integrals abstract in this paper the authors established hermite hadamard s inequalities for harmonically convex functions via fractional integrals and obtained some hermite hadamard type inequalities of these classes of functions

improvement of some ostrowski gruss type inequalities abstract in this paper we improve and further generalize some ostrowski gruss type inequalities involving bounded once and twice differentiable mappings

a generalization of two sharp inequalities in two independent variables a generalization of two sharp inequalities of simpson type and ostrowski type in two independent variables is established

lattice solitary wave solutions of discrete nonlinear wave equations using a direct method it is shown that the real exponential approach to the solutions of nonlinear evolution and wave equations can also he applied to discrete systems as examples the lattice solitary wave and kink solutions of the discrete modified kdv dmkdv equation and some modified versions of this equation are derived using this approach

lattice fractional diffusion equation in terms of a riesz caputo difference abstract a fractional difference is defined by the use of the right and the left caputo fractional differences the definition is a two sided operator of riesz type and introduces back and forward memory effects in space difference then a fractional difference equation method is suggested for anomalous diffusion in discrete finite domains a lattice fractional diffusion equation is proposed and the numerical simulation of the diffusion process is discussed for various difference orders the result shows that the riesz difference model is particularly suitable for modeling complicated dynamical behaviors on discrete media

some generalized ostrowski gruss type integral inequalities in this paper we establish some new ostrowski gruss type integral inequalities involving k 1 interior points in 1d case which are generalizations of some known results in the literature and one of which is sharp then we deduce an ostrowski gruss type integral inequality in 2d case involving k 1 2 interior points for the first time we also present one application on the estimate of error bound for numerical integration formula in which a sharp error bound for a new numerical integration formula is provided by the results established

hermite hadamard and hermite hadamard fejer type inequalities for generalized fractional integrals abstract in this paper we obtain the hermite hadamard and hermite hadamard fejer type inequalities for fractional integrals which generalize the two familiar fractional integrals namely the riemann liouville and the hadamard fractional integrals into a single form we prove that in most cases we obtain the riemann liouville and the hadamard equivalence just by taking limits when a parameter 1 and 0 respectively

new inequalities of ostrowski type for mappings whose derivatives are s convex in the second sense via fractional integrals a new identity similar to an identity proved in alomari et al 2010 15 for fractional integrals is established then by making use of the established identity some new ostrowski type inequalities for riemann liouville fractional integral are established our results have some relationships with the results of alomari et al 2010 proved in 15 and the analysis used in the proofs is simple

a note to inequalities of euler gruss type following the main ideas of wang 1 we generalize matie s results and establish our inequalities for functions with n t h derivatives of bounded p variation all of our error bounds are sharp in the sense that they cannot be replaced by smaller ones

positive solutions for a system of fractional differential equations with coupled integral boundary conditions we investigate the existence of positive solutions for a system of nonlinear riemann liouville fractional differential equations with coupled integral boundary conditions

sharp inequalities of simpson type and ostrowski type two sharp inequalities are derived the first is a sharp simpson s inequality and the second is a sharp inequality of ostrowski type the mentioned inequalities give error bounds for some known quadrature rules these results enlarge applicability email protected the corresponding quadrature rules with respect to the obtained error bounds applications in numerical integration are also given

the construction of exact multiple pole solutions of some 2 1 dimensional integrable nonlinear evolution equations via the dressing method the exact multiple pole solutions of several 2 1 dimensional integrable nonlinear evolution equations such as the kadomtsev petviashvili equation the modified kadomtsev petviashvili equation and the davey stewartson system of equations and others by the use of the dressing method are constructed

on some generalizations of an ostrowski gruss type integral inequality in this paper we improve and extend a new ostrowski gruss type integral inequality obtained recently by feng and meng 2012 26 to be precise we show that a condition imposed on the inequality can be removed furthermore we provide a two dimensional generalization of this ostrowski gruss type inequality which is sharp

bounds for the chebyshev functional and applications to the weighted integral formulae the aim of this paper is to provide some error estimates for the general weighted n point quadrature formulae by using some inequalities for the chebyshev functional the above results are applied to obtain some new bounds for the gauss chebyshev formulae of the first and the second kind

an explicit expression of the dark n soliton solution of the mkdv equation by means of the darboux transformation a darboux transformation is developed for generating dark multi soliton solutions of the mkdv equation the darboux matrices are found explicitly in recursive manner and a system of linear algebraic equations is derived for determining the dark n soliton solutions by means of the binet cauchy formula an explicit expression of the dark n soliton solution is obtained

hermite hadamard hermite hadamard fejer dragomir agarwal and pachpatte type inequalities for convex functions via new fractional integrals abstract the aim of this paper is to establish hermite hadamard hermite hadamard fejer dragomir agarwal and pachpatte type inequalities for new fractional integral operators with exponential kernel these results allow us to obtain a new class of functional inequalities which generalizes known inequalities involving convex functions furthermore the obtained results may act as a useful source of inspiration for future research in convex analysis and related optimization fields

construction of solutions of the sine gordon equation by means of fredholm determinants abstract a new straightforward and rigorous approach to the theory of the sine gordon equation is presented it provides a simple and unified view of the three known methods for solution namely hirota s method of generating n soliton solutions the inverse scattering transform and backlund transformations in addition new types of solutions corresponding to multiple poles in the scattering data can be easily obtained the principal tool used is the theory of fredholm determinants generalisations to other soliton equations seem to be possible

an inequality of ostrowski gruss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules abstract in this paper we derive a new inequality of ostrowski gruss type and apply it to the estimation of error bounds for some special means and for some numerical quadrature rules

positive solutions of three point boundary value problems for systems of nonlinear second order ordinary differential equations abstract in this paper we study the three point boundary value problems for systems of nonlinear second order ordinary differential equations of the form u f t v t 0 1 v g t u t 0 1 u 0 v 0 0 u u 1 v v 1 under some conditions we show the existence and multiplicity of positive solutions of the above problem by applying the fixed point index theory in cones

on ostrowski type inequalities for stieltjes integrals with absolutely continuous integrands and integrators of bounded variation some ostrowski type inequalities are given for the stieltjes integral where the integrand is absolutely continuous while the integrator is of bounded variation the case when f is convex is explored applications for the mid point rule and a generalised trapezoid type rule are also presented

the fredholm determinant method for the kdv equations abstract the fredholm determinant method is a new and rigorous way to investigate soliton equations and to construct their solutions it consists essentially of establishing a comparatively simple relation between the soliton equation and its linearized form the inverse scattering method hirota s method of constructing n soliton solutions and backlund transformations are given a new and unified interpretation moreover some new results can be obtained in this paper the fredholm determinant method is applied to the korteweg de vries kdv modified kdv and the hierarchy of generalized kdv equations

improvement and further generalization of inequalities of ostrowski gruss type abstract we improve some inequalities of ostrowski gruss type and further generalize them we apply the obtained results to the estimation of error bounds for some numerical quadrature rules also some bounds for the differences of some special means are discussed

solvability and numerical simulations for bvps of fractional coupled systems involving left and right fractional derivatives abstract we study the three point boundary value problems for the fractional differential coupled systems with both left and right fractional derivatives in the paper firstly the upper lower solutions method for the systems is presented and some existence results to the systems solutions are also obtained secondly we also give out an iterative approach for finding approximate solutions of the systems finally we consider a concrete example where we obtain the existence result of the solution and also give out its numerical solution and the graphical simulation

inequalities of hermite hadamard type involving an s convex function with applications in the paper the authors establish some integral inequalities of hermite hadamard type involving the product of an s convex function and a symmetric function and apply these new established inequalities to construct inequalities for special means

a unified approach to some inequalities of ostrowski gruss type based on the euler maclaurin formula in the spirit of 1 we provide a unified approach to some inequalities of ostrowski gruss type which include some existing results as special cases some illustrative examples are also included

properties of h convex functions related to the hermite hadamard fejer inequalities in this paper we prove the hermite hadamard fejer inequalities for an h convex function and we point out the results for some special classes of functions also some generalization of the hermite hadamard inequalities and some properties of functions h and f which are naturally joined to the h convex function are given finally applications on p logarithmic mean and mean of the order p are obtained

systems of riemannliouville fractional equations with multi point boundary conditions we study the existence and multiplicity of positive solutions for a system of nonlinear riemannliouville fractional differential equations subject to multi point boundary conditions which contain fractional derivatives the nonsingular and singular cases are investigated

the ostrowski s integral inequality for lipschitzian mappings and applications abstract a generalization of ostrowski s inequality for lipschitzian mappings and applications in numerical analysis and for euler s beta function are given

generalizations of weighted ostrowski type inequalities for mappings of bounded variation and their applications abstract in this paper we establish some generalizations of weighted ostrowski type inequalities

on euler trapezoid formulae modified versions of the euler trapezoid formula for functions whose derivatives are either functions of bounded variation or lipschitzian functions or functions in l p spaces are given the results are applied to quadrature formulae

on the generalization of ostrowski and gruss type discrete inequalities abstract the main purpose of this paper is to establish a generalization of discrete inequalities of the ostrowski and gruss type involving two functions the analysis used in the proofs is fairly elementary

on new inequalities of hermite hadamard fejer type for convex functions via fractional integrals in this paper we establish some weighted fractional inequalities for differentiable mappings whose derivatives in absolute value are convex these results are connected with the celebrated hermite hadamard fejer type integral inequality the results presented here would provide extensions of those given in earlier works

gruss and ostrowski type inequalities abstract in this paper we use a method originated in s s dragomir some gruss type inequalities in inner product spaces j inequal pure appl math 4 2 2003 article 42 to establish some gruss and ostrowski type inequalities

on new general integral inequalities for s convex functions in this paper the authors establish some new estimates for the remainder term of the midpoint trapezoid and simpson formula using functions whose derivatives in absolute value at certain power are s convex some applications to special means of real numbers are provided as well

approximations to large amplitude solitary waves on nonlinear electrical lattices abstract in this paper we describe an approximate method to characterise solitary wave solutions of nonlinear lattice equations it is based upon one and two point pade approximations to a series of the real exponential travelling wave solutions of the underlying dispersive system the theory is applied to an example of a lattice system which models an experimental nonlinear transmission line and the results obtained are consistent with numerical simulations even for relatively large amplitude solitary waves the speed amplitude relation is investigated and compared with the derived using quasi continuum methods