5: Paper Source
PDF document

Paper's Title:

**
Analysis of a Frictional Contact Problem for Viscoelastic Piezoelectric Materials**

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**
Author(s):

**Meziane Said Ameur, Tedjani Hadj Ammar and Laid Maiza**

Departement of Mathematics,

El Oued University,

P.O. Box 789, 39000 El Oued,

Algeria.

E-mail:
said-ameur-meziane@univ-eloued.dz

Departement of Mathematics,

El Oued University,

P.O. Box 789, 39000 El Oued,

Algeria.

E-mail:
hadjammar-tedjani@univ-eloued.dz

Department of Mathematics,

Kasdi Merbah University,

30000 Ouargla,

Algeria.

E-mail: maiza.laid@univ-ouargla.dz

Abstract:

In this paper, we consider a mathematical model that describes
the quasi-static process of contact between two thermo-electro-viscoelastic bodies with damage and adhesion. The damage of the materials caused by elastic deformations. The contact is frictional and modeled with a normal compliance condition involving adhesion effect of contact surfaces. Evolution of the
bonding field is described by a first order differential equation. We derive variational formulation for the model and prove an existence and uniqueness result of the weak solution. The proof is based on arguments of evolutionary variational inequalities, parabolic inequalities, differential equations, and fixed point theorem.

1: Paper Source
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Paper's Title:

**
Hermite-Hadamard Type Inequalities for ***k*-Riemann Liouville Fractional Integrals Via Two Kinds of Convexity

Author(s):

**R. Hussain**^{1}, A. Ali^{2}, G. Gulshan^{3}, A. Latif^{4} and K. Rauf^{5}

^{1,2,3,4}Department
of Mathematics,

Mirpur University of Science and Technology, Mirpur.

Pakistan.

E-mail^{1}:
rashida12@gmail.com

E-mail^{2}:
unigraz2009@yahoo.com

E-mail^{3}:
ghazalagulshan@yahoo.com

E-mail^{4}:
asialatif87@gmail.com

^{5}Department
of Mathematics,

University of Ilorin, Ilorin,

Nigeria.

E-mail^{5}:
krauf@unilorin.edu.ng

Abstract:

In this article, a fundamental integral identity including the first order
derivative of a given function via *k*-Riemann-Liouville fractional integral is established. This is used to obtain further Hermite-Hadamard type inequalities involving left-sided and right-sided
*k*-Riemann-Liouville fractional integrals for *m*-convex and *(s,m)*-convex functions respectively.

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