Fractional Integrodifferential Equations

Top PDF Fractional Integrodifferential Equations:

Lyapunov stability solutions of fractional integrodifferential equations

Lyapunov stability solutions of fractional integrodifferential equations

In recent papers [7, 8], we used Schauder’s fixed-point theorem to obtain local exis- tence, and Tychonov’s fixed-point theorem to obtain global existence of solution of the fractional integrodifferential equations (1.1) and (1.2). The existence of extremal (maxi- mal and minimal) solutions of the fractional integrodiffrential equations (1.1) and (1.2) using comparison principle and Ascoli lemma has been investigated in [9].

5 Read more

Existence of Mild Solutions to Fractional Integrodifferential Equations of Neutral Type with Infinite Delay

Existence of Mild Solutions to Fractional Integrodifferential Equations of Neutral Type with Infinite Delay

We study the solvability of the fractional integrodifferential equations of neutral type with infinite delay in a Banach space X. An existence result of mild solutions to such problems is obtained under the conditions in respect of Kuratowski’s measure of noncompactness. As an application of the abstract result, we show the existence of solutions for an integrodifferential equation.

15 Read more

Existence and Approximate Solutions for Nonlinear Hybrid Fractional Integrodifferential Equations

Existence and Approximate Solutions for Nonlinear Hybrid Fractional Integrodifferential Equations

Therefore, the main result of this paper also includes the existence as well as approximation results for the solutions of above mentioned initial value problems of fractional differential equations as special cases. Again our approach here in this paper is different than that employed in the related paper of Dhage [3].

11 Read more

Nonlocal cauchy problem for delay fractional integrodifferential equations of neutral type

Nonlocal cauchy problem for delay fractional integrodifferential equations of neutral type

integrodifferential equations of neutral type with finite delay and nonlocal conditions in a Banach space X . The existence of mild solutions is proved by means of measure of noncompactness. As an application, the existence of mild solutions for some integrodifferential equation is obtained.

23 Read more

Existence of solutions for impulsive fractional integrodifferential equations with mixed boundary conditions

Existence of solutions for impulsive fractional integrodifferential equations with mixed boundary conditions

noncompactness, we discuss the existence of solutions for a boundary value problem of impulsive integrodifferential equations of fractional order α ∈ (1, 2]. Our results improve and generalize some known results in (Zhou and Chu in Commun. Nonlinear Sci. Numer. Simul. 17:1142-1148, 2012; Bai et al. in Bound. Value Probl. 2016:63, 2016). Finally, an example is given to illustrate that our result is valuable.

19 Read more

Weak solutions nonlinear fractional integrodifferential equations in nonreflexive Banach spaces

Weak solutions nonlinear fractional integrodifferential equations in nonreflexive Banach spaces

The aim of this paper is to discuss the existence of weak solutions for a nonlinear two-point boundary value problem of integrodifferential equations of fractional order α ∈ (1, 2]. Our analysis relies on the Krasnoselskii fixed point theorem combined with the technique of measure of weak noncompactness.

13 Read more

Existence result for neutral fractional integrodifferential equations with nonlocal integral boundary conditions

Existence result for neutral fractional integrodifferential equations with nonlocal integral boundary conditions

In this article, we study a neutral fractional integrodifferential equation supplemented with nonlocal flux type integral boundary conditions. The existence and uniqueness results are obtained by using Banach fixed point theorem and Leray-Schauder nonlinear alternative theorem. The obtained results are illustrated by examples at the end.

7 Read more

Interval fractional integrodifferential equations without singular kernel by fixed point in partially ordered sets

Interval fractional integrodifferential equations without singular kernel by fixed point in partially ordered sets

that the large number of fractional derivatives does not constitute a disadvantage, since they can be used in different models which provide the best reflection of the behavior of the system. In many simultaneously occurring processes in modeling of the real world phenomena to obtain data, the field observations are needed. The modeling of a dynamical system based on the field observations becomes uncertain and vagueness or fuzziness, which is inherent in the systems behavior rather than being purely random or deterministic. The study of interval and fuzzy differential equations is an area of mathematics that has recently received a lot of attention (see e.g. [4, 11, 17, 18, 19, 20]). Recently, there are some papers dealing with the existence of solution for nonlinear set valued and fuzzy fractional differential equations whose methods are based on the monotone method, the method of upper and lower solutions and fixed point theorems [1, 2, 5, 6, 7, 10, 17]. Among of them, we can find results on existence of solution for fuzzy differential equations in presence of

18 Read more

Existence Results for Nonlinear Boundary Value Problems of Fractional Integrodifferential Equations with Integral Boundary Conditions

Existence Results for Nonlinear Boundary Value Problems of Fractional Integrodifferential Equations with Integral Boundary Conditions

This paper deals with some existence results for a boundary value problem involving a nonlinear integrodi ff erential equation of fractional order q ∈ 1, 2 with integral boundary conditions. Our results are based on contraction mapping principle and Krasnosel’ski˘ ı’s fixed point theorem. Copyright q 2009 B. Ahmad and J. J. Nieto. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

11 Read more

Existence and Uniqueness of Mild Solutions for Fractional Integrodifferential Equations

Existence and Uniqueness of Mild Solutions for Fractional Integrodifferential Equations

[26] J. Liang and T-J. Xiao, “Solvability of the Cauchy problems for infinite delay equations”, Nonlinear Analysis: Theory, Methods & Applications, vol.58, no.3-4, 2004, pp.271-297. [27] A.Pazy, Semigroups of Linear Operators and Applications to

6 Read more

On existence and uniqueness of fractional integrodifferential equations with an integral fractional boundary condition

On existence and uniqueness of fractional integrodifferential equations with an integral fractional boundary condition

β < 1 is the Riemann-Liouville fractional integral of order β . The theory of fractional calculus has been available and applicable to various fields of study. The investigation of the theory of fractional differential and integral equations has started quite recently. One can see the monographs of Kil- bas et.al. [11], Podlubny [15]. Integrodifferential equations arise in many engineering and scientific disciplines, often as approximation to partial differential equations, which repre- sent much of the continuum phenomena. Integrodifferential equation is an equation that the unknown function appears un- der the sign of integration and it also contains the derivatives of the unknown function. It can be classified into Fredholm equations and Volterra equations. The upper bound of the region for integral part of Volterra type is variable, while it is a fixed number for that of Fredholm type. However, in this paper, we focus on Fredholm integrodifferential equations.

7 Read more

Solutions to Riemann–Liouville fractional integrodifferential equations via fractional resolvents

Solutions to Riemann–Liouville fractional integrodifferential equations via fractional resolvents

Recently some interesting results on Caputo fractional resolvents have been given in [11, 12, 26]. We note that the properties of resolvent operators for Caputo derivative and Riemann–Liouville derivative are different in essence, though neither of them has the semigroup property. For Caputo fractional resolvents T α (t), T α (0)x = x for every x ∈ X,

17 Read more

Solvability of Nonautonomous Fractional Integrodifferential Equations with Infinite Delay

Solvability of Nonautonomous Fractional Integrodifferential Equations with Infinite Delay

We study the existence and uniqueness of mild solution of a class of nonlinear nonautonomous fractional integrodifferential equations with infinite delay in a Banach space X. The existence of mild solution is obtained by using the theory of the measure of noncompactness and Sadovskii’s fixed point theorem. An application of the abstract results is also given.

18 Read more

An abstract partial functional integrodifferential equations

An abstract partial functional integrodifferential equations

Eq.(1.1) is the mixed type of Eq.(1.3) and Eq.(1.4). It well enable us to study the nonlinear Volterra integrodifferential equation with delay. On the basis of the results in Eq.(1.4) we gen- eralize the method used in [33] to derive global existence and regularity of Eq.(1.1). The result obtained is a generalization and a continuation of [33]. The method used treats the equation in the domain of A with the graph norm employing results from linear semigroup theory concern- ing abstract inhomogeneous linear differential equations.

17 Read more

Integrodifferential Inequality for Stability of Singularly Perturbed Impulsive Delay Integrodifferential Equations

Integrodifferential Inequality for Stability of Singularly Perturbed Impulsive Delay Integrodifferential Equations

with impulsive initial conditions and derived some sufficient conditions ensuring the exponential stability of solutions for the singular perturbed impulsive delay differential equations SPIDDEs. In this paper, we will improve the inequality established in 14 such that it is effective for SPIDIDEs. By establishing an IDIDI, some sufficient conditions ensuring the exponential stability of any solution of SPIDIDEs for sufficiently small ε > 0 are obtained. The results extend and improve the earlier publications, and which will be shown by the Remarks 3.2 and 3.5 provided later. An example is given to illustrate the theory.

11 Read more

A Characterization of Semilinear Surjective Operators and Applications to Control Problems

A Characterization of Semilinear Surjective Operators and Applications to Control Problems

In this section we consider some control systems gov- erned by partial differential equations, integrodifferential equations and difference equations that can study using these results. Particularly, we work in details the con- trolled damped wave equation. Finally, we propose fu- ture investigations an open problem.

9 Read more

Boundary Controllability of Nonlinear Fractional Integrodifferential Systems

Boundary Controllability of Nonlinear Fractional Integrodifferential Systems

Let E and U be a pair of real Banach spaces with norms · and | · |, respectively. Let σ be a linear closed and densely defined operator with Dσ ⊆ E and let τ ⊆ X be a linear operator with Dσ and Rτ ⊆ X, a Banach space. In this paper we study the boundary controllability of nonlinear fractional integrodifferential systems in the form

9 Read more

Convergence for Hyperbolic Singular Perturbation of Integrodifferential Equations

Convergence for Hyperbolic Singular Perturbation of Integrodifferential Equations

[18] G. W. Desch, R. Grimmer, and W. Schappacher, “Propagation of singularities by solutions of second order integrodifferential equations,” in Volterra Integrodifferential Equations in Banach Spaces and Applications (Trento, 1987), G. Da Prato and M. Iannelli, Eds., vol. 190 of Pitman Research Notes in Mathematics Series, pp. 101–110, Longman Scientific & Technical, Harlow, UK, 1989.

11 Read more

Global existence for some neutral functional integrodifferential equations with finite delay

Global existence for some neutral functional integrodifferential equations with finite delay

real world applications, wherever (in physics, chemistry, biology, medecine, economy etc, see e.g, [16]) the evolution of a process depends on its history in an essentiel way. In recent year, the theory of integrodifferential equations with delay has been studied deeply in the literature. For more details, we refer to [2], [3], [5], [6], [7], [8], [9], [10], [17] and the references therein. In this paper, we are interested in the existence and regularity of solutions for the following neutral partial functional integrodifferential equation with finite delay

14 Read more

Fractional Evolution Integrodifferential Systems with Nonlocal Conditions in Banach Spaces

Fractional Evolution Integrodifferential Systems with Nonlocal Conditions in Banach Spaces

(2.1) By a local mild solution of (1.1) on we mean that there exist a and a function defined from into such that is a mild solution of (1.1) refer to [8,22,25]. We define the fractional power by

5 Read more

Show all 10000 documents...