Affiliation:
1. MVGR College of Engineering
2. Andhra University
Abstract
The aim of this paper is to determine the eigenvalue intervals of $\mu_{\mathtt{k}},~1\le \mathtt{k}\le \mathtt{n}$ for which an iterative system of a class of fractional-order differential equations with parameterized integral boundary conditions (BCs) has at least one positive solution by means of standard fixed point theorem of cone type. To the best of our knowledge, this will be the first time that we attempt to reach such findings for the topic at hand in the literature. The obtained results in the paper are illustrated with an example of their feasibility.
Publisher
Universal Journal of Mathematics and Applications
Reference35 articles.
1. [1] H. G. Sun, Y. Zhang, D. Baleanu, W. Chen, Y. Q. Chen, A new collection of real world applications of fractional calculus in science and engineering, Commun. Nonlinear Sci. Numer. Simul., 64 (2018), 213–231.
2. [2] A. A. Kilbas, H. M. Srivasthava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, vol. 204, Elsevier, Amsterdam, 2006.
3. [3] I. Podulbny, Fractional Differential Equations, Academic Press, San Diego, 1999.
4. [4] E. F. D. Goufo, A biomathematical view on the fractional dynamics of cellulose degradation, Fract. Calc. Appl. Anal., 18(3) (2015), 554–564.
5. [5] H. H. Sherief, M. A. el-Hagary, Fractional order theory of thermo-viscoelasticity and application, Mech. Time-Depend Mater., 24 (2020), 179–195.