Author:
Ghaderi Mehran,Rezapour Shahram
Abstract
AbstractRecent research indicates the need for improved models of physical phenomena with multiple shocks. One of the newest methods is to use differential inclusions instead of differential equations. In this work, we intend to investigate the existence of solutions for an m-dimensional system of quantum differential inclusions. To ensure the existence of the solution of inclusions, researchers typically rely on the Arzela–Ascoli and Nadler’s fixed point theorems. However, we have taken a different approach and utilized the endpoint technique of the fixed point theory to guarantee the solution’s existence. This sets us apart from other researchers who have used different methods. For a better understanding of the issue and validation of the results, we presented numerical algorithms, tables, and some figures. The paper ends with an example.
Publisher
Springer Science and Business Media LLC
Reference49 articles.
1. Hilfer, R.: Experimental evidence for fractional time evolution in glass forming materials. Chem. Phys. 284(1–2), 399–408 (2002). https://doi.org/10.1016/S0301-0104(02)00670-5
2. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)
3. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)
4. Fabrizio, M., Giorgi, C., Pata, V.: A new approach to equations with memory. Arch. Ration. Mech. Anal. 198(1), 189–232 (2010). https://doi.org/10.1007/s00205-010-0300-3
5. Agarwal, R., Hristova, S., Regan, D.O.: Integral presentations of the solution of a boundary value problem for impulsive fractional integro-differential equations with Riemann–Liouville derivatives. AIMS Math. 7, 2973–2988 (2022). https://doi.org/10.3934/math.2022164