Advanced Functional Evolution Equations and Inclusions

Benchohra, Mouffak; Abbas, Saı̈d

doi:10.1007/978-3-319-17768-7

Cited by 48 publications

(34 citation statements)

References 100 publications

(202 reference statements)

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“…Evolution equations arise in many areas of applied mathematics [1,2]. This type of equations have received a lot of attention in recent years [3]. There are many results concerning second-order di erential equations, see for example Fattorini [4], and Travis and Webb [5].…”

Section: Y( ) = G(y) Y ( ) = H(y)mentioning

confidence: 99%

Second order evolution equations with nonlocal conditions

Benchohra

Nieto

Rezoug

2017

Demonstratio Mathematica

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Section: Y( ) = G(y) Y ( ) = H(y)mentioning

confidence: 99%

Second order evolution equations with nonlocal conditions

Benchohra

Nieto

Rezoug

2017

Demonstratio Mathematica

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“…To establish existence of solutions has been a very active research area in mathematics. This is particularly true with respect to existence of solutions for fractional differential equations [2], which is also explained by the development of other fields of research, such as physics, mechanics and biology [1,15,30]. Many methods are used to prove existence of a solution, such as the fixed point technique, for which several theories are available [3,4,8].…”

Section: A Nonlinear Fractional Voigt Modelmentioning

confidence: 99%

Linear and Nonlinear Fractional Voigt Models

Chidouh

Guezane-Lakoud

Bebbouchi

et al. 2016

Lecture Notes in Electrical Engineering

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We consider fractional generalizations of the ordinary differential equation that governs the creep phenomenon. Precisely, two Caputo fractional Voigt models are considered: a rheological linear model and a nonlinear one. In the linear case, an explicit Volterra representation of the solution is found, involving the generalized Mittag-Leffler function in the kernel. For the nonlinear fractional Voigt model, an existence result is obtained through a fixed point theorem. A nonlinear example, illustrating the obtained existence result, is given.

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“…The theory and application of integrodifferential equations are important subjects in applied mathematics, see, for example [1][2][3][4][5][6][7][8] and recent development of the topic, see the monographs of [9]. In recent times there have been an increasing interest in studying the abstract autonomous second order, see for example [10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Second Order Semilinear Volterra-Type Integro-Differential Equations with Non-Instantaneous Impulses

et al. 2019

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We consider a non-instantaneous system represented by a second order nonlinear differential equation in a Banach space E. We use the family of linear bounded operators introduced by Kozak, Darbo fixed point method and Kuratowski measure of noncompactness. A new set of sufficient conditions is formulated which guarantees the existence of the solution of the non-instantaneous system. An example is also discussed to illustrate the efficiency of the obtained results.

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Advanced Functional Evolution Equations and Inclusions

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Cited by 48 publications

References 100 publications

Second order evolution equations with nonlocal conditions

Second order evolution equations with nonlocal conditions

Linear and Nonlinear Fractional Voigt Models

Second Order Semilinear Volterra-Type Integro-Differential Equations with Non-Instantaneous Impulses

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