Acta mathematica scientia,Series B ›› 2015, Vol. 35 ›› Issue (3): 601-609.doi: 10.1016/S0252-9602(15)30006-0

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ON SOLVABILITY OF THE INTEGRODIFFERENTIAL HYPERBOLIC EQUATION WITH PURELY NONLOCAL CONDITIONS

Ahcene MERAD1, Abdelfatah BOUZIANI2, Cenap OZEL3, Adem KILIÇMAN4   

  1. 1. Department of Mathematics, Larbi Ben M'hidi University, Oum El Bouaghi, Algeria;
    2. Department of Mathematics, Larbi Ben M'hidi University, Oum El Bouaghi, Algeria;
    3. Department of Mathematics, Faculty of Science, Dokuz Eylul University 35160 Buca/I.zmir, Turkey;
    4. Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, UPM, Serdang, Selangor, 43400, Malaysia
  • Received:2013-12-30 Online:2015-05-01 Published:2015-05-01
  • Supported by:

    The fourth author gratefully acknowledges the partially support by the University Putra Malaysia under the Grant Scheme having project number GP-IBT/2013/9420100.

Abstract:

In this study, we prove the existence, uniqueness, and continuous dependence upon the data of solution to integro-differential hyperbolic equation with purely nonlocal (integral) conditions. The proofs are based on a priori estimates and Laplace transform method. Finally, we obtain the solution using a numerical technique (Stehfest algorithm) by inverting the Laplace transform.

Key words: Integro-differential hyperbolic equation, approximate solution, nonlocal purely conditions

CLC Number: 

  • 44A10
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