Abstract
The fixed point theorem of Guo–Krasnosel’skii is applied in this paper to find the intervals of the parameters \({{\lambda }_{1}},{{\lambda }_{2}}, \ldots ,{{\lambda }_{m}}\) that have a positive solution to an iterative system of nth order fractional differential equation with three-point boundary conditions including a nonhomogeneous term.
REFERENCES
New Trends in Fractional Differential Equations with Real-World Applications in Physics, Ed. by J. Singh, J. Y. Hristov, and Z. Hammouch (Frontiers Media SA, Lausanne, 2020).
K. N. Nishimoto, Fractional Calculus and Its Applications (Nihon Univ., Koriyama, 1990).
K. S. Miller and B. Ross, (Wiley, New York, 1993).
I. Podlubny, Fractional Differential Equations (Academic, New York, 1999).
A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations (Elsevier, Boston, 2006).
A. M. Lopes and L. Chen, “Fractional order systems and their applications,” Fractal Fractional 6, 389 (2022). https://doi.org/10.3390/fractalfract6070389
J. Henderson and S. K. Ntouyas, “Positive solutions for system of nth order three-point nonlocal boundary value problems,” Electron. J. Qual. Theory Differ. Equations, No. 18, 1–12 (2007).
J. Henderson, S. K. Ntouyas, and I. K. Purnaras, “Positive solutions for systems of generalized three-point nonlinear boundary value problems,” Comment. Math. Univ. Carolinae 49, 79–91 (2008).
J. Henderson, S. K. Ntouyas, and I. K. Purnaras, “Positive solutions for systems of second order four-point nonlinear boundary value problems,” Comm. Appl. Anal. 12, 29–40 (2008).
K. R. Prasad, N. Sreedhar, and K. R. Kumar, “Solvability of iterative systems of three-point boundary value problems,” TWMS J. Appl. Eng. Math. 3, 147–159 (2013).
K. R. Prasad, M. Rashmita, and N. Sreedhar, “Solvability of higher order three-point iterative systems,” Ufimsk. Mat. Zh. 12 (3), 109–124 (2020).
N. Sreedhar, N. Kanakayya, and K. Prasad, “Solvability of higher order iterative system with non-homogeneous integral boundary conditions,” Contemp. Math. 3, 141–161 (2022). https://doi.org/10.37256/cm.3220221300
K. R. Prasad and B. M. B. Krushna, “Eigenvalues for iterative systems of Sturm-Liouville fractional order two-point boundary value problems,” Fractional Calc. Appl. Anal. 17, 638–653 (2014). https://doi.org/10.2478/s13540-014-0190-4
K. R. Prasad, B. M. B. Krushna, and N. Sreedhar, “Eigenvalues for iterative systems of (n, p)-type fractional order boundary value problem,” Int. J. Anal. Appl. 5, 136–146 (2014).
K. R. Prasad and B. M. B. Krushna, “Positive solutions to iterative systems of fractional order three-point boundary value problems with Riemann-Liouville derivative,” Fractional Differ. Calculus 5, 137–150 (2015). https://doi.org/10.7153/fdc-05-12
D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones (Academic, Orlando, Fla., 1988).
M. A. Krasnosel’skii, Positive Solutions of Operator Equations (P. Noordhoff, Groningen, 1964).
ACKNOWLEDGMENTS
The authors would like to thank the referees for their insightful remarks and suggestions.
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
The authors declare that they have no conflicts of interest.
About this article
Cite this article
Prasad, K.R., Sreedhar, N. & Rashmita, M. Solvability of Iterative System of Fractional Order Differential Equations with Nonhomogeneous Boundary Conditions. Russ Math. 67, 63–76 (2023). https://doi.org/10.3103/S1066369X23060099
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066369X23060099