Fractional Order Pettis Integral Equations with Multiple Time Delay in Banach Spaces

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Mouffak Benchohra ◽  
Fatima-Zohra Mostefai
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Time Delay ◽  
Banach Spaces ◽  
Fractional Order ◽  
Existence Of Solutions ◽  
Multiple Time ◽  
Pettis Integral ◽  
Measure Of Weak Noncompactness ◽  
Pettis Integrability

Abstract This paper is devoted to study the existence of solutions under the Pettis integrability assumption for an integral equation of fractional order with multiple time delay in Banach space by using the technique of measure of weak noncompactness. Mathematics Subject Classification 2010: 26A33, 34A08.

scholarly journals A Note on the Paper ”Fractional Order Pettis Integral Equations with Multiple Time Delay in Banach Spaces” by M. Benchohra and F.-Z. Mostefai

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
Mieczysław Cichoń
Keyword(s):  
Integral Equation ◽  
Time Delay ◽  
Banach Spaces ◽  
Integral Equations ◽  
Fractional Order ◽  
Weak Topology ◽  
Classical Case ◽  
Existence Results ◽  
Multiple Time ◽  
Pettis Integral

Abstract On a recent paper Benchohra and Mostefai [2] presented some existence results for an integral equation of fractional order with multiple time delay in Banach spaces. In contrast to the classical case, when assumptions are expressed in terms of the strong topology, they considered another case, namely with the weak topology. It has some consequences for the proof. We present here some comments and corrections.

scholarly journals Solvability of functional-integral equations (fractional order) using measure of noncompactness

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Reza Arab ◽  
Hemant Kumar Nashine ◽  
N. H. Can ◽  
Tran Thanh Binh
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Integral Equations ◽  
Fractional Order ◽  
Measure Of Noncompactness ◽  
Functional Integral ◽  
Arbitrary Measure ◽  
Functional Integral Equations

AbstractWe investigate the solutions of functional-integral equation of fractional order in the setting of a measure of noncompactness on real-valued bounded and continuous Banach space. We introduce a new μ-set contraction operator and derive generalized Darbo fixed point results using an arbitrary measure of noncompactness in Banach spaces. An illustration is given in support of the solution of a functional-integral equation of fractional order.

scholarly journals Integrable Solutions of a Nonlinear Integral Equation via Noncompactness Measure and Krasnoselskii's Fixed Point Theorem

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Mahmoud Bousselsal ◽  
Sidi Hamidou Jah
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Nonlinear Integral Equations ◽  
Measure Of Weak Noncompactness ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Noncompactness Measure

We study the existence of solutions of a nonlinear Volterra integral equation in the space L1[0,+∞). With the help of Krasnoselskii’s fixed point theorem and the theory of measure of weak noncompactness, we prove an existence result for a functional integral equation which includes several classes on nonlinear integral equations. Our results extend and generalize some previous works. An example is given to support our results.

Semilinear fractional order integro-differential inclusions with infinite delay

2018 ◽  
Vol 25 (3) ◽  
pp. 317-327 ◽  
Author(s):  
Khalida Aissani ◽  
Mouffak Benchohra ◽  
Mohamed Abdalla Darwish
Keyword(s):  
Banach Spaces ◽  
Fractional Order ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Multivalued Maps ◽  
Nonlinear Alternative

AbstractIn this paper, we study the existence of mild solutions for a class of semilinear fractional order integro-differential inclusions with infinite delay in Banach spaces. Sufficient conditions for the existence of solutions are derived by using a nonlinear alternative of Leray–Schauder type for multivalued maps due to Martelli. An example is given to illustrate the theory.

On solutions of a stochastic integral equation of the volterra type with applications for chemotherapy

1988 ◽  
Vol 25 (02) ◽  
pp. 257-267 ◽  
Author(s):  
D. Szynal ◽  
S. Wedrychowicz
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Stochastic Model ◽  
Asymptotic Behaviour ◽  
Existence Of Solutions ◽  
Stochastic Integral ◽  
Volterra Type ◽  
Stochastic Integral Equation

This paper deals with the existence of solutions of a stochastic integral equation of the Volterra type and their asymptotic behaviour. Investigations of this paper use the concept of a measure of non-compactness in Banach space and fixed-point theorem of Darbo type. An application to a stochastic model for chemotherapy is also presented.

scholarly journals On a local degree for a class of multi-valued vector fields in infinite dimensional Banach spaces

1996 ◽  
Vol 1 (4) ◽  
pp. 381-396 ◽  
Author(s):  
N. M. Benkafadar ◽  
B. D. Gel'man
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Vector Fields ◽  
Existence Of Solutions ◽  
Index Zero ◽  
Compact Mapping ◽  
Infinite Dimensional ◽  
Upper Semicontinuous ◽  
Local Degree

This paper is devoted to the development of a local degree for multi-valued vector fields of the formf−F. Here,fis a single-valued, proper, nonlinear, Fredholm,C1-mapping of index zero andFis a multi-valued upper semicontinuous, admissible, compact mapping with compact images. The mappingsfandFare acting from a subset of a Banach spaceEinto another Banach spaceE1. This local degree is used to investigate the existence of solutions of a certain class of operator inclusions.

scholarly journals Pettis integrability of fuzzy mappings with values in arbitrary Banach spaces

2017 ◽  
Vol 67 (6) ◽  
Author(s):  
Luisa Di Piazza ◽  
Valeria Marraffa
Keyword(s):  
Banach Spaces ◽  
Pettis Integral ◽  
Fuzzy Mapping ◽  
Pettis Integrability

AbstractIn this paper we study the Pettis integral of fuzzy mappings in arbitrary Banach spaces. We present some properties of the Pettis integral of fuzzy mappings and we give conditions under which a scalarly integrable fuzzy mapping is Pettis integrable.

scholarly journals Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces

2005 ◽  
Vol 2005 (17) ◽  
pp. 2769-2774
Author(s):  
Anna Kisiolek ◽  
Ireneusz Kubiaczyk
Keyword(s):  
Banach Space ◽  
Asymptotic Behaviour ◽  
Banach Spaces ◽  
Difference Equations ◽  
Measure Of Noncompactness ◽  
Nonlinear Difference Equations ◽  
Measure Of Weak Noncompactness ◽  
Delay Difference Equations ◽  
Delay Difference ◽  
Nonlinear Delay

We consider the second-order nonlinear difference equations of the formΔ(rn−1Δxn−1)+pnf(xn−k)=hn. We show that there exists a solution(xn), which possesses the asymptotic behaviour‖xn−a∑j=0n−1(1/rj)+b‖=o(1),a,b∈ℝ. In this paper, we extend the results of Agarwal (1992), Dawidowski et al. (2001), Drozdowicz and Popenda (1987), M. Migda (2001), and M. Migda and J. Migda (1988). We suppose thatfhas values in Banach space and satisfies some conditions with respect to the measure of noncompactness and measure of weak noncompactness.

scholarly journals On solutions of fractional multi-term sequential problems via some special categories of functions and (AEP)-property

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Dumitru Baleanu ◽  
Muhammad Qamar Iqbal ◽  
Azhar Hussain ◽  
Sina Etemad ◽  
Shahram Rezapour
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fractional Integral ◽  
Existence Of Solutions ◽  
Existence Theory ◽  
New Techniques ◽  
Fractional Integral Equation ◽  
Contraction Maps ◽  
Special Category

AbstractThe main intention of this article is that new techniques of existence theory are used to derive some required criteria pertinent to a given fractional multi-term problem and its inclusion version. In such an approach, we do our research on a fractional integral equation corresponding to the mentioned BVPs. In more precise words, by virtue of this integral equation, we construct new operators which belong to a special category of functions named α-admissible and α-ψ-contraction maps coupled with operators having (AEP)-property. Next, by considering some new properties on the existing Banach space having properties (B) and $(C_{\alpha })$ ( C α ) , our argument for ensuring the existence of solutions is completed. In addition, we also add two simulative examples to review our findings by a numerical view.

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