Abstract
AbstractIn this paper, we consider the biparabolic problem under nonlocal conditions with both linear and nonlinear source terms. We derive the regularity property of the mild solution for the linear source term while we apply the Banach fixed-point theorem to study the existence and uniqueness of the mild solution for the nonlinear source term. In both cases, we show that the mild solution of our problem converges to the solution of an initial value problem as the parameter epsilon tends to zero. The novelty in our study can be considered as one of the first results on biparabolic equations with nonlocal conditions.
Funder
National Research Foundation of Korea
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference34 articles.
1. Adigüzel, R.S., Aksoy, U., Karapinar, E., Erhan, I.M.: On the solution of a boundary value problem associated with a fractional differential equation. Math. Methods Appl. Sci., 1–12 (2020). https://doi.org/10.1002/mma.6652
2. Adigüzel, R.S., Aksoy, U., Karapinar, E., Erhan, I.M.: On the solutions of fractional differential equations via Geraghty type hybrid contractions. Appl. Comput. Math. 20(2), 313–333 (2021)
3. Adigüzel, R.S., Aksoy, U., Karapinar, E., Erhan, I.M.: Uniqueness of solution for higher-order nonlinear fractional differential equations with multi-point and integral boundary conditions. Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 115(3), 155 (2021)
4. Alaoui, A.L., Azroul, E., Hamou, A.A.: Monotone iterative technique for nonlinear periodic time fractional parabolic problems. Adv. Theory Nonlinear Anal. Appl. 4(3), 194–213 (2020) 2020
5. Besma, K., Nadji, B., Faouzia, R.: A modified quasi-boundary value method for an abstract ill-posed biparabolic problem. Open Math. 15, 1649–1666 (2017)