Fractional Differential Equations with Memory

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In this presentation we discuss some issues about fractional partial differential equations of order between one and two appearing in viscoelasticity and thermoelasticity. In particular, we will look at simple strings, Euleur-Bernoulli beams and Timoshenko beams although our
arguments apply to many other types of problems. First, we justify the passage from integer order to fractional order. Then, we show how to prove well-posedness of the systems. Next, we establish some stability results. The main challenges and the difficulties encountered when dealing with the memory terms will be highlighted.

Brief Biography

Nasser-eddine Tatar is a Professor at the Department of Mathematics, King Fahd University of Petroleum & Minerals. His areas of research interest are: Partial Differential Equations of Parabolic Type and Hyperbolic Type, Integro-Differential Equations and Inequalities, Fractional Differential Equations and Neural Network Theory. He is in the editorial board of many international journals and he is recipient of several awards.