Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 16 (2021), 301 -- 325

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EXISTENCE RESULTS FOR A FUNCTIONAL INTEGRO-DIFFERENTIAL INCLUSIONS WITH RIEMANN-STIELTJES INTEGRAL OR INFINITE-POINT BOUNDARY CONDITIONS

A. M. A. El-Sayed, Sh. M Al-Issa and M. H. Hijazi

Abstract. In this article, we establish the existence of solutions for initial value problem of fractional-order differential inclusion with nonlocal infinite-point or Riemann–Stieltjes integral boundary conditions. The continuous dependence of the solution on the set of selections and some other functions will be proved.

2020 Mathematics Subject Classification: 34A127; 4H10; 45G10
Keywords: Functional integro-differential inclusion; fixed point theorem; Riemann–Stieltjes integral boundary conditions; infinite-point boundary conditions

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A. M. A. EL-Sayed
Department of Mathematics, Alexandria University, Alexandria, Egypt.
e-mail: amasayed@alexu.edu.eg

Sh. M Al-Issa
Department of Mathematics, Lebanese International University, Beirut, Lebanon,
Department of Mathematics, International University of Beirut, Saida, Lebanon.
e-mail: Shorouk.alissa@liu.edu.lb

M. H. Hijazi
Department of Mathematics, Lebanese International University, Beirut, Lebanon.
e-mail: 31330579@students.liu.edu.lb



http://www.utgjiu.ro/math/sma