يمكنكم ارسال مقالاتكم عبر البريد الالكتروني jscience@ush.sd

العدد التاسع

Application on Approximate Controllability of Semi-Linear Neutral Integro-Differential Equations with Nonlocal Conditions

Abdalkarim Siddig Ahmed and shawgy Hussein

Abdalkarim Siddig Ahmed Abdelrahman (1) and shawgy Hussein(2)

1Shendi University Faculty of Education, Department of Mathematics, Sudan. Email: alkahli2935@ush.sd

2Sudan University of Science and Technology, College of Science, Department of Mathematics, Sudan.

Email: Shawgy2020@gmail.com


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Abstract

For validity we show an applicationon the approximate controllability of a semi-linear neutral integrodifferential equation with nonlocal conditions by theory of analytic semi-groups, fractional powers of operators, and resolvent operator theory,considered by Hai Huang and Xianlong Fu1 [1]. Under the assumption of controllability on the corresponding linear system, we obtain the sufficient conditions for the considered semi-linear integro-differential system. In particular, the compactness condition or Lipschitz condition for the function g in the nonlocal condition appearing in literature is not required here. An example is also provided to illustrate the application of the obtained results.
Keywords: Neutral integro-differential equation, Approximate controllability, Resolvent operator, Fractional power operator, Nonlocal condition system.

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