Some results on existence and uniqueness of solutions for fractional boundary value problems
Authors
S. Almuthaybiri
- Department of Mathematics, College of Science, Qassim University, Saudi Arabia.
Abstract
The purpose of this work is to improve Ferreira’s results [R. A. C. Ferreira, Electron J. Differ. Equ., \({\bf 2016}\) (2016), 5 pages]. The advancement is achieved through an application of Rus's contraction mapping theorem. To this end, we derive new estimates for integrals involving Green’s function. Applying these estimates in conjunction with Rus’s contraction mapping theorem demonstrates that a larger class of fractional boundary value problems admit a unique solution than those obtained by Ferreira. We conclude this article with numerical validation with applications, that highlight the nature and significance of the advancements made.
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ISRP Style
S. Almuthaybiri, Some results on existence and uniqueness of solutions for fractional boundary value problems, Journal of Mathematics and Computer Science, 40 (2026), no. 3, 405--414
AMA Style
Almuthaybiri S., Some results on existence and uniqueness of solutions for fractional boundary value problems. J Math Comput SCI-JM. (2026); 40(3):405--414
Chicago/Turabian Style
Almuthaybiri, S.. "Some results on existence and uniqueness of solutions for fractional boundary value problems." Journal of Mathematics and Computer Science, 40, no. 3 (2026): 405--414
Keywords
- Fractional boundary value problem
- existence and uniqueness of solutions
- Rus's contraction mapping theorem
- nonlinear equations
- numerical estimates
MSC
References
-
[1]
S. S. Almuthaybiri, C. C. Tisdell, Sharper Existence and Uniqueness Results for Solutions to Third-Order Boundary Value Problems, Math. Model. Anal., 25 (2020), 409–420
-
[2]
S. S. Almuthaybiri, C. C. Tisdell, Sharper existence and uniqueness results for solutions to fourth-order boundary value problems and elastic beam analysis, Open Math., 18 (2020), 1006–1024
-
[3]
S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133–181
-
[4]
R. A. C. Ferreira, Existence and uniqueness of solutions for two-point fractional boundary value problems, Electron J. Differ. Equ., 2016 (2016), 5 pages
-
[5]
S. R. Grace, G. N. Chhatria, S. Kaleeswari, Y. Alnafisah, O. Moaaz, Forced-Perturbed Fractional Differential Equations of Higher Order: Asymptotic Properties of Non-Oscillatory Solutions, Fractal Fract., 9 (2025), 12 pages
-
[6]
O. Holder, Ueber einen Mittelwertsatz (German), J. Goett. Nachr., (1889), 38–47
-
[7]
W. G. Kelley, A. C. Peterson, The theory of differential equations, Springer, New York (2010)
-
[8]
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier Science B.V., Amsterdam (2006)
-
[9]
W. N. Li, On the forced oscillation of certain fractional partial differential equations, Appl. Math. Lett., 50 (2015), 5–9
-
[10]
A. P. Prudnikov, Y. A. Brychkov, O. I. Marichev, Integrals and series. Vol. 3, Gordon and Breach Science Publishers, New York (1990)
-
[11]
E. D. Rainville, Special Functions, The Macmillan Company, New York (1960)
-
[12]
L. J. Rogers, An extension of a certain theorem in inequalities, Messenger of Math., 17 (1888), 145–150
-
[13]
I. A. Rus, On a fixed point theorem of Maia, Studia Univ. Babe¸s-Bolyai Math., 22 (1977), 40–42
-
[14]
S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional integrals and derivatives, Gordon and Breach Science Publishers, Yverdon (1993)
-
[15]
L. J. Slater, Generalized hypergeometric functions, Cambridge University Press, Cambridge (1966)
-
[16]
C. P. Stinson, S. S. Almuthaybiri, C. C. Tisdell, A note regarding extensions of fixed point theorems involving two metrics via an analysis of iterated functions, ANZIAM J., 61 (2019), C15–C30
-
[17]
A. Zaidi, S. Almuthaybiri, Explicit evaluations of subfamilies of the hypergeometric function 3F2(1) along with specific fractional integrals, AIMS Math., 10 (2025), 5731–5761
