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Existence and Uniqueness of Solutions for Time-Fractional Oldroyd-B Fluid Equations with Generalized Fractional Derivatives
  
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KeyWord:Time-fractional Oldroyd-B fluid equations, generalized fractional derivatives, generalized Laplace transform, regularity, Banach fixed point theorem
Author NameAffiliation
Hassan Messaoudi Laboratory of Informatics and Mathematics, University of Souk-Ahras, P.O. Box 1553, Souk-Ahras, 41000, Algeria 
Abdelouaheb Ardjouni Department of Mathematics and Informatics, University of Souk-Ahras, P.O. Box 1553, Souk-Ahras, 41000, Algeria 
Salah Zitouni Laboratory of Informatics and Mathematics, University of Souk-Ahras, P.O. Box 1553, Souk-Ahras, 41000, Algeria 
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Abstract:
      In this paper, we study the existence and uniqueness of solutions for time-fractional Oldroyd-B fluid equations with generalized fractional derivatives. We distinguish two cases. Firstly for the linear case, we get regularity results under some hypotheses of the source function and the initial data. Secondly for the nonlinear case, we use the Banach fixed point theorem to obtain the existence and uniqueness of solutions.