A priori estimate for resolving the boundary fractional problem

Hacene Mecheri; Maryam G. Alshehri; Hacene Mecheri; Maryam G. Alshehri

doi:10.3934/math.2023037

AIMS Mathematics

2023, Volume 8, Issue 1: 765-774. doi: 10.3934/math.2023037

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A priori estimate for resolving the boundary fractional problem

Hacene Mecheri ^{1
,
,},
Maryam G. Alshehri ^{2
,
,}

1.
Mathematics and Informatics Department, LAMIS, Laboratory Tebessa University, Algeria
2.
Mathematics Department, Faculty of Science, University of Tabuk, 71491, Saudi Arabia

Received: 20 February 2022 Revised: 12 June 2022 Accepted: 20 June 2022 Published: 12 October 2022
MSC : 76D03, 76N10

The energy inequality method (or a priori estimation) known in classical cases has been adopted for fractional evolution equations associated with initial conditions and boundary integral conditions. We prove the existence and uniqueness of the solution to the problem described in the following.
- existence and uniqueness,
- solvability,
- fractional equation,
- integral conditions,
- Caputo derivatives
Citation: Hacene Mecheri, Maryam G. Alshehri. A priori estimate for resolving the boundary fractional problem[J]. AIMS Mathematics, 2023, 8(1): 765-774. doi: 10.3934/math.2023037

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Abstract

The energy inequality method (or a priori estimation) known in classical cases has been adopted for fractional evolution equations associated with initial conditions and boundary integral conditions. We prove the existence and uniqueness of the solution to the problem described in the following.

References

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