Qualitative Study on \(\psi-\)Caputo fractional differential inclusion with non-local conditions and feedback control
Volume 34, Issue 3, pp 295--312
https://dx.doi.org/10.22436/jmcs.034.03.08
Publication Date: April 02, 2024
Submission Date: September 10, 2023
Revision Date: February 20, 2024
Accteptance Date: February 27, 2024
Authors
Sh. M. Al-Issa
- Faculty of Arts and Sciences, Department of Mathematics, Lebanese International University, Saida, Lebanon.
- Faculty of Arts and Sciences, Department of Mathematics, The International University of Beirut, Alexandria, Beirut, Lebanon.
A. M. A. El-Sayed
- Faculty of Sciences, Department of Mathematics, Alexandria University, Alexandria, Egypt.
I. H. Kaddoura
- Faculty of Arts and Sciences, Department of Mathematics, Lebanese International University, Saida, Lebanon.
- Faculty of Arts and Sciences, Department of Mathematics, The International University of Beirut, Beirut, Lebanon.
F. H. Sheet
- Faculty of Arts and Sciences, Department of Mathematics, Lebanese International University, Saida, Lebanon.
Abstract
This article discuss the existence of solutions for certain classes of nonlinear \(\psi\)–Caputo fractional derivative differential inclusion via a nonlocal infinite-point or Riemann–Stieltjes integral boundary conditions and with a feedback control in Banach spaces. Our approach is based on Schauder's fixed point theorem.
We establish appropriate conditions that guarantee unique solutions and demonstrate that the solution continuously depends on the set of selections and some other functions. Additionally, we include {example} to illustrate the key findings.
Share and Cite
ISRP Style
Sh. M. Al-Issa, A. M. A. El-Sayed, I. H. Kaddoura, F. H. Sheet, Qualitative Study on \(\psi-\)Caputo fractional differential inclusion with non-local conditions and feedback control, Journal of Mathematics and Computer Science, 34 (2024), no. 3, 295--312
AMA Style
Al-Issa Sh. M., El-Sayed A. M. A., Kaddoura I. H., Sheet F. H., Qualitative Study on \(\psi-\)Caputo fractional differential inclusion with non-local conditions and feedback control. J Math Comput SCI-JM. (2024); 34(3):295--312
Chicago/Turabian Style
Al-Issa, Sh. M., El-Sayed, A. M. A., Kaddoura, I. H., Sheet, F. H.. "Qualitative Study on \(\psi-\)Caputo fractional differential inclusion with non-local conditions and feedback control." Journal of Mathematics and Computer Science, 34, no. 3 (2024): 295--312
Keywords
- \(\psi\)-Caputo fractional operator
- Riemann-Stieltjes integral boundary conditions
- infinite-point boundary conditions
- feedback control
MSC
References
-
[1]
T. Abdeljawad, N. Mlaiki, M. S. Abdo, Caputo-type fractional systems with variable order depending on the impulses and changing the kernel, Fractals, 30 (2022), 15 pages
-
[2]
N. Adjimi, A. Boutiara, M. S. Abdo, M. Benbachir, Existence results for nonlinear neutral generalized Caputo fractional differential equations, J. Pseudo-Differ. Oper. Appl., 12 (2021), 17 pages
-
[3]
H. Afshari, M. S. Abdo, J. Alzabut, Further results on existence of positive solutions of generalized fractional boundary value problems, Adv. Difference Equ., 2020 (2020), 13 pages
-
[4]
B. Ahmad, S. K. Ntouyas, Nonlocal fractional boundary value problems with slit-strips boundary conditions, Fract. Calc. Appl. Anal., 18 (2015), 261–280
-
[5]
S. M. Al-Issa, A. M. A. El-Sayed, H. H. G. Hashem, An Outlook on Hybrid Fractional Modeling of a Heat Controller with Multi-Valued Feedback Control, Fractal Fract., 7 (2023), 1–19
-
[6]
R. Almeida, A Caputo fractional derivative of a function with respect to another function, Commun. Nonlinear Sci. Numer. Simul., 44 (2017), 460–481
-
[7]
J.-P. Aubin, A. Cellina, Differential inclusion, Springer-Verlag, Berlin (1984)
-
[8]
Z. Bai, T. Qiu, Existence of positive solution for singular fractional differential equation, Appl. Math. Comput., 215 (2009), 2761–2767
-
[9]
M. Caputo, Linear models of dissipation whose Q is almost frequency independent. II, Geophys. J. R. Astr. Soc., 13 (1967), 529–539
-
[10]
A. Cellina, S. Solimini, Continuous extension of selection, Bull. Polish Acad. Sci. Math., 35 (1987), 573–581
-
[11]
F. Chen, The permanence and global attractivity of Lotka-Volterra competition system with feedback controls, Nonlinear Anal. Real World Appl., 7 (2006), 133–143
-
[12]
R. F. Curtain, A. J. Pritchard, Functional analysis in modern applied mathematics, Academic Press, London-New York (1977)
-
[13]
K. Deimling, Nonlinear functional Analysis, Springer-Verlag, Berlin (1985)
-
[14]
A. M. A. El-Sayed, A. G. Ibrahim, Multivalued fractional differential equations, Appl. Math. Comput., 68 (1995), 15–25
-
[15]
A. M. A. El-Sayed, A.-G. Ibrahim, Set-valued integral equations of fractional-orders, Appl. Math. Comput., 118 (2001), 113–121
-
[16]
A. M. A. El-Sayed, Sh. M Al-Issa, Monotonic integrable solution for a mixed type integral and differential inclusion of fractional orders, Int. J. Differ. Equ. Appl., 18 (2019), 1–9
-
[17]
A. M. A. El-Sayed, Sh. M Al-Issa, Monotonic solutions for a quadratic integral equation of fractional order, AIMS Math., 4 (2019), 821–830
-
[18]
A. M. A. El-Sayed, Sh. M Al-Issa, M. H. Hijazi, Existence results for a functional integro-differential inclusions with Riemann-Stieltjes integral or infinite-point boundary conditions, Surv. Math. Appl., 16 (2021), 301–325
-
[19]
H. H. G. Hashem, A. M. A. El-Sayed, S. M. Al-Issa, Investigating Asymptotic Stability for Hybrid Cubic Integral Inclusion with Fractal Feedback Control on the Real Half-Axis, Fractal Fract., 7 (2023), 16 pages
-
[20]
M. D. Kassim, T. Abdeljawad, W. Shatanawi, S. M. Ali, M. S. Abdo, A qualitative study on generalized Caputo fractional integro-differential equations, Adv. Difference Equ., 2021 (2021), 18 pages
-
[21]
A. N. Kolomogorov, S. V. Fom¯ın, Introductory real analysis, Dover Publications, Inc., New York (1975)
-
[22]
N. Kosmatov, A singular boundary value problem for nonlinear differential equations of fractional order, J. Appl. Math. Comput., 29 (2009), 125–135
-
[23]
K. Kuratowski, C. Ryll-Nardzewski, A general theorem on selectors, Bull. Acad. Polon. Sci. S´er. Sci. Math. Astronom. Phys., 13 (1965), 397–403
-
[24]
O. Melkemi, M. S. Abdo, M. A. Aiyashi, M. D. Albalwi, On the global well-posedness for a hyperbolic model arising from chemotaxis model with fractional Laplacian operator, J. Math., 2023 (2023), 10 pages
-
[25]
P. Nasertayoob, Solvability and asymptotic stability of a class of nonlinear functional-integral equation with feedback control, Commun. Nonlinear Anal., 5 (2018), 19–27
-
[26]
P. Nasertayoob, S. M. Vaezpour, Positive periodic solution for a nonlinear neutral delay population equation with feedback control, J. Nonlinear Sci. Appl., 6 (2013), 152–161
-
[27]
H. M. Srivastava, A. M. A. El-Sayed, F. M. Gaafar, A Class of Nonlinear Boundary Value Problems for an Arbitrary Fractional-Order Differential Equation with the Riemann-Stieltjes Functional Integral and Infinite-Point Boundary Conditions, Symmetry, 10 (2018), 13 pages