Abstract
AbstractSome fundamental conditions and hypotheses are established to ensure the existence, uniqueness, and stability to a class of implicit boundary value problems (BVPs) with Atangana–Baleanu–Caputo type derivative and integral. The required results are established by utilizing the Banach contraction mapping principle and fixed point theorem of Krasnoselskii. In addition, various types of stability results including Hyers–Ulam, generalized Hyers–Ulam, Hyers–Ulam–Rassias, and generalized Hyers–Ulam–Rassias stability are formulated for the problem under consideration. Pertinent examples are given to justify the results we obtain.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference39 articles.
1. Ross, B.: The development of fractional calculus 1695–1900. Hist. Math. 4(1), 75–89 (1977)
2. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. North-Holand, Amsterdam (2006)
3. Arfan, M., Shah, K., Abdeljawad, T., Mlaiki, N., Ullah, A.: A Caputo power law model predicting the spread of the COVID-19 outbreak in Pakistan. Alex. Eng. J. 60(1), 447–456 (2021)
4. Ahmad, S., Ullah, A., Al-Mdallal, Q.M., Khan, H., Shah, K., Khan, A.: Fractional order mathematical modeling of COVID-19 transmission. Chaos Solitons Fractals 139, 110256 (2020)
5. Moulai-Khatir, A., Remili, M., Beldjerd, D.: Stability, boundedness and square integrability of solutions to certain third order neutral delay differential equations. Palest. J. Math. 9(2), 880–890 (2020)
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