On a boundary value problem of arbitrary orders differential inclusion with nonlocal, integral and infinite points boundary conditions

A. M. A. El-Sayed; W. G. El-Sayed; Somyya S. Amrajaa; A. M. A. El-Sayed; W. G. El-Sayed; Somyya S. Amrajaa

doi:10.3934/math.2022215

AIMS Mathematics

2022, Volume 7, Issue 3: 3896-3911. doi: 10.3934/math.2022215

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Research article

On a boundary value problem of arbitrary orders differential inclusion with nonlocal, integral and infinite points boundary conditions

1.
Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt
2.
Faculty of Science, Omar al mukhtar University, Libya

Received: 11 August 2021 Accepted: 24 November 2021 Published: 10 December 2021
MSC : 26A33, 34K45, 47G10

In this work, we are concerned with a boundary value problem of fractional orders differential inclusion with nonlocal, integral and infinite points boundary conditions. We prove some existence results for that nonlocal boundary value problem. Next, the existence of maximal and minimal solutions is proved. Finally, the sufficient condition for the uniqueness and continuous dependence of solution are studied.
- differential inclusion,
- boundary value problem,
- existence of solutions,
- continuous dependence
Citation: A. M. A. El-Sayed, W. G. El-Sayed, Somyya S. Amrajaa. On a boundary value problem of arbitrary orders differential inclusion with nonlocal, integral and infinite points boundary conditions[J]. AIMS Mathematics, 2022, 7(3): 3896-3911. doi: 10.3934/math.2022215

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Abstract

In this work, we are concerned with a boundary value problem of fractional orders differential inclusion with nonlocal, integral and infinite points boundary conditions. We prove some existence results for that nonlocal boundary value problem. Next, the existence of maximal and minimal solutions is proved. Finally, the sufficient condition for the uniqueness and continuous dependence of solution are studied.

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