The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces

In this paper we prove the existence of solutions of certain kinds of nonlinear fractional integrodifferential equations in Banach spaces. Further, Cauchy problems with nonlocal initial conditions are discussed for the aforementioned fractional integrodifferential equations. At the end, an example is presented.     

Extreme solutions of initial value problems for nonlinear second order integrodifferential equations in Banach spaces

1. IntroductionIn paPer l1], Guo Da jun established the eristence of extreme solutions of initnd Vaueproblems fOr first order illtegrodmerelltial eqllations of VOlterra type in Banach spaces.Now, in this paPer, we consider the IVP for second order illtegrodifferelltial equatinns onthe infinite iliterVa R in BanaCh space E:U" = F(t, u,u', Tu), Vt E R , u(0) = xo, u'(0) = x1) (1)where xo,x1 E E,F E C(R x E x E x E,E), and(Tx)(t) = l'k(,,.).(.)d., Vt E R , (2)jok E C(fl, R ), fl…     

Existence results for fractional impulsive integrodifferential equations in Banach spaces

This paper is mainly concerned with the existence of solutions of first order nonlinear impulsive fractional integrodifferential equations in Banach spaces. The results are obtained by using fixed point principles. Further, some interesting examples are presented to illustrate the theory.     

Callocation methods for volterra integrodifferential equations with singular kernels

A collocation method which uses Hermite cubic elements is proposed for the solution of Volterra integrodifferential equations with singular kernels. Optimum error estimates in the uniform norm are obtained by means of interpolation operators. We also report on results of numerical comparisons with one well established method and another new “modified collocation” scheme.     

Regularization methods for nonlinear Ill-posed equations involving m-accretive mappings in Banach spaces

In this paper we prove strong convergence of the Browder-Tikhonov regularization method and the regularization inertial proximal point algorithm to a solution of nonlinear ill-posed equations involving m-accretive mappings in real, reflexive, and strictly convex Banach spaces with a uniformly Gâteaux differentiable norm without weak sequential continuous duality mapping.     

Existence of solutions of nonlinear integrodifferential equations of sobolev type with nonlocal condition in Banach spaces

In this paper we prove the existence of mild and strong solutions of a nonlinear integrodifferential equation of Sobolev type with nonlocal condition. The results are obtained by using semigroup theory and the Schauder fixed point theorem.     

Remark on the existence results for fractional impulsive integrodifferential equations in Banach spaces

This paper deal with the study of the existence of solutions of nonlinear fractional integrodifferential equations with impulsive conditions in Banach spaces, by means of fixed point principle. The purpose of the paper is to generalize the results of [5] and correct an error in the example included in [5].     

Nonlocal Cauchy problem for delay integrodifferential equations of Sobolev type in Banach spaces

In this paper, we prove the existence of mild and strong solutions of nonlinear time varying delay integrodifferential equations of Sobolev type with nonlocal conditions in Banach spaces. The results are obtained by using the theory of compact semigroups and Schaefer's fixed-point theorem.     

Weak solutions for nonlinear functional equations in Banach spaces

Summary Some existence theorems for abstract differential equations in Banach spaces are given. Durante lo svolgimento di questo lavoro, l'autore ha usufruito di una borsa di ricerca presso l'Istituto per le Applicazioni del Calcolo del C.N.R. — Roma. Entrata in Redazione l'll febbraio 1970.     

Decay characteristics for nonlinear differential equations in Banach spaces

A standard procedure for optimizing the transient response of a system of nonlinear differential equations near an asymptotically stable equilibrium point involves choosing the system parameters so that the right-most eigenvalue of the linearized system is furthest to the left in the complex plane. This procedure is shown to also apply for nonlinear systems in infinite dimensional Banach spaces.     

A class of fractional delay nonlinear integrodifferential controlled systems in Banach spaces

We study a class of fractional delay nonlinear integrodifferential controlled systems associated with analytic semigroup in Banach spaces. Existence of α-mild solutions and optimal controls are obtained. Lastly, an example is presented to illustrate our abstract results.     

Existence and regularity of solutions for some partial functional integrodifferential equations in Banach spaces

In this work, we study the existence and regularity of solutions for some partial functional integrodifferential equations in Banach spaces. We suppose that the undelayed part admits a resolvent operator in the sense given by Grimmer in [R. Grimmer, Resolvent operators for integral equations in a Banach space, Transaction of American Mathematical Society 273 (1982) 333–349]. The delayed part is assumed to be locally Lipschitz. Firstly, we show the existence of the mild solutions. Secondly, we give sufficient conditions ensuring the existence of the strict solutions.     

Numerical methods for singular nonlinear integro-differential equations

For the numerical integration of singular nonlinear integro-differential equations we consider fractional linear multistep methods. We prove convergence of these methods and discuss their stability (as an extension of A-stability for stiff differential equations). Numerical experiments with the Basset equation are included.     

Existence of positive solution for second-order nonlinear impulsive singular differential equations of mixed type in Banach spaces

In this paper, by constructing a closed convex set and using the fixed point theory of completely continuous operators, we investigate the existence of positive solutions for an initial value problem of second-order nonlinear impulsive singular integro-differential equations in a Banach space. The method used in this paper is different from that in the literature.     

Projection methods for the solution of one class of singular integrodifferential equations

In this paper we propose a computational scheme of the general projection method for the solution of singular integrodifferential equations in the theory of stream lines and thermal conductivity. We theoretically substantiate this scheme from the standpoint of the theory of approximate methods of functional analysis. We consider particular cases of the general projection method, namely, the method of moments and the collocation method.