Abstract
<abstract><p>This paper discusses the existence of solutions for fractional differential equations with nonlocal boundary conditions (NFDEs) under essential assumptions. The boundary conditions incorporate a point $ 0\leq c < d $ and fixed points at the end of the interval $ [0, d] $. For $ i = 0, 1 $, the boundary conditions are as follows: $ a_{i}, b_{i} > 0 $, $ a_{0} p(c) = -b_{0} p(d), \ a_{1} p^{'}(c) = -b_{1} p^{'}(d) $. Furthermore, the research aims to expand the usability and comprehension of these results to encompass not just NFDEs but also classical fractional differential equations (FDEs) by using the Krasnoselskii fixed-point theorem and the contraction principle to improve the completeness and usefulness of the results in a wider context of fractional differential equations. We offer examples to demonstrate the results we have achieved.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference14 articles.
1. I. Podlubny, Fractional differential equations, In: Mathematics in science and engineering, Elsevier, 198 (1999).
2. S. Abbas, M. Benchohra, G. M. N'Guerekata, Topics in fractional differential equations, New York: Springer, 2012. https://doi.org/10.1007/978-1-4614-4036-9
3. D. R. Smart, Fixed point theorems, Cambridge University Press, 1980.
4. Y. Zhou, Fractional evolution equations and inclusions: Analysis and control, Academic Press, 2016. https://doi.org/10.1016/C2015-0-00813-9
5. A. Ali, I. Suwan, T. Abdeljawad, Abdullah, Numerical simulation of time partial fractional diffusion model by Laplace transform, AIMS Mathematics, 7 (2022), 2878–2890. https://doi.org/10.3934/math.2022159
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