Existence and controllability results for neutral fractional Volterra-Fredholm integro-differential equations
Volume 34, Issue 4, pp 361--380
https://dx.doi.org/10.22436/jmcs.034.04.04
Publication Date: April 05, 2024
Submission Date: December 05, 2023
Revision Date: December 24, 2023
Accteptance Date: February 21, 2024
Authors
Th. Gunasekar
- Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R\(\&\)D Institute of Science and Technology, Chennai-600062, Tamil Nadu, India.
- School of Artificial Intelligence and Data Science, Indian Institute of Technology (IIT), Jodhpur 342030, India.
P. Raghavendran
- Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R\(\&\)D Institute of Science and Technology, Chennai 600062, Tamil Nadu, India.
Sh. S. Santra
- Department of Mathematics, JIS College of Engineering, Kalyani, West Bengal 741235, India.
M. Sajid
- Department of Mechanical Engineering, College of Engineering, Qassim University, Buraydah 51452, Saudi Arabia.
Abstract
This paper delves into the investigation of a Volterra-Fredholm integro-differential equation enhanced with Caputo fractional derivatives subject to specific order conditions. The study rigorously establishes the existence of solutions through the application of the Schauder fixed-point theorem. Furthermore, it encompasses neutral Volterra-Fredholm integro-differential equations, thereby extending the applicability of the findings. In addition, the paper explores the concept of controllability for the obtained solutions, offering valuable insights into how these solutions behave over extended time periods.
Share and Cite
ISRP Style
Th. Gunasekar, P. Raghavendran, Sh. S. Santra, M. Sajid, Existence and controllability results for neutral fractional Volterra-Fredholm integro-differential equations, Journal of Mathematics and Computer Science, 34 (2024), no. 4, 361--380
AMA Style
Gunasekar Th., Raghavendran P., Santra Sh. S., Sajid M., Existence and controllability results for neutral fractional Volterra-Fredholm integro-differential equations. J Math Comput SCI-JM. (2024); 34(4):361--380
Chicago/Turabian Style
Gunasekar, Th., Raghavendran, P., Santra, Sh. S., Sajid, M.. "Existence and controllability results for neutral fractional Volterra-Fredholm integro-differential equations." Journal of Mathematics and Computer Science, 34, no. 4 (2024): 361--380
Keywords
- Volterra-Fredholm integro-differential equations
- fractional derivatives
- controllability
- Schauder fixed point theorem
MSC
- 26A33
- 26D10
- 34A12
- 45G10
- 45J05
- 47G20
References
-
[1]
R. P. Agarwal, C. Zhang, T. Li, Some remarks on oscillation of second order neutral differential equations, Appl. Math. Comput., 274 (2016), 178–181
-
[2]
B. Ahmad, S. Sivasundaram, Some existence results for fractional integro-differential equations with nonlinear conditions, Commun. Appl. Anal., 12 (2008), 107–112
-
[3]
J. Alzabut, S. R. Grace, J. M. Jonnalagadda, S. S. Santra, B. Abdalla, Higher-order Nabla Difference Equations of Arbitrary Order with Forcing, Positive and Negative Terms: Non-oscillatory Solutions, Axioms, 12 (2023), 1–14
-
[4]
A. Atangana, D. Baleanu, New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model, arXiv preprint arXiv:1602.03408, 20 (2016), 763–769
-
[5]
M. Bohner, T. Li, Oscillation of second-order p-Laplace dynamic equations with a nonpositive neutral coefficient, Appl. Math. Lett., 37 (2014), 72–76
-
[6]
M. Caputo, M. Fabrizio, A new definition of fractional derivative without singular kernel, Prog. Fract. Differ. Appl., 1 (2015), 73–85
-
[7]
D. N. Chalishajar, Controllability of mixed Volterra-Fredholm-type integro-differential systems in Banach space, J. Franklin Inst., 344 (2007), 12–21
-
[8]
A. Columbu, S. Frassu, G. Viglialoro, Properties of given and detected unbounded solutions to a class of chemotaxis models, Stud. Appl. Math., 151 (2023), 1349–1379
-
[9]
Z. Dahmani, A. Taeb, New existence and uniqueness results for high dimensional fractional differential systems, Facta Univ. Ser. Math. Inform., 30 (2015), 281–293
-
[10]
C. Dineshkumar, V. Vijayakumar, R. Udhayakumar, A. Shukla, K. S. Nisar, Controllability discussion for fractional stochastic Volterra-Fredholm integro-differential systems of order 1 < r < 2, Int. J. Nonlinear Sci. Numer. Simul., 24 (2023), 1947–1979
-
[11]
M. Fe˘ckan, J. Wang, M. Posp´ıˇsil, Fractional-order equations and inclusions, De Gruyter, Berlin (2017)
-
[12]
A. Ganesh, S. Deepa, D. Baleanu, S. S. Santra, O. Moaaz, V. Govindan, R. Ali, Hyers-Ulam-Mittag-Leffler stability of fractional differential equations with two Caputo derivative using fractional Fourier transform, AIMS Math., 7 (2022), 1791–1810
-
[13]
T. Gunasekar, P. Raghavendran, The Mohand Transform Approach to Fractional Integro-Differential Equations, J. Comput. Anal. Appl., 33 (2024), 358–371
-
[14]
T. Gunasekar, J. Thiravidarani, M. Mahdal, P. Raghavendran, A. Venkatesan, M. Elangovan, Study of Non-Linear Impulsive Neutral Fuzzy Delay Differential Equations with Non-Local Conditions, Mathematics, 11 (2023), 1–16
-
[15]
H. HamaRashid, H. M. Srivastava, M. Hama, P. O. Mohammed, M. Y. Almusawa, D. Baleanu, Novel algorithms to approximate the solution of nonlinear integro-differential equations of Volterra-Fredholm integro type, AIMS Math., 8 (2023), 14572–14591
-
[16]
A. Hamoud, Existence and uniqueness of solutions for fractional neutral Volterra-Fredholm integro differential equations, Adv. Theory Nonlinear Anal. Appl., 4 (2020), 321–331
-
[17]
A. A. Hamoud, K. P. Ghadle, Some new uniqueness results of solutions for fractional Volterra-Fredholm integrodifferential equations, Iran. J. Math. Sci. Inform., 17 (2022), 135–144
-
[18]
A. Hamoud, N. Mohammed, K. Ghadle, Existence and uniqueness results for Volterra-Fredholm integro differential equations, Adv. Theory Nonlinear Anal. Appl., 4 (2020), 361–372
-
[19]
S. Harikrishnan, D. Vivek, E. M. Elsayed, Existence and Stability of Integro Differential Equation with Generalized Proportional Fractional Derivative, Izv. Nats. Akad. Nauk Armenii Mat., 58 (2023), 24–35
-
[20]
K. Hattaf, A new generalized definition of fractional derivative with non-singular kernel, Computation, 8 (2020), 1–9
-
[21]
E. Hern´andez M., D. O. Regan, Controllability of Volterra-Fredholm type systems in Banach spaces, J. Franklin Inst., 346 (2009), 95–101
-
[22]
C. Jayakumar, S. S. Santra, D. Baleanu, R. Edwan, V. Govindan, A. Murugesan, M. Altanji, Oscillation Result for Half-Linear Delay Difference Equations of Second Order, Math. Biosci. Eng., 19 (2022), 3879–3891
-
[23]
V. Jurdjevic, J. P. Quinn, Controllability and stability, J. Differential Equations, 28 (1978), 381–389
-
[24]
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier Science B.V., Amsterdam (2006)
-
[25]
T. Li, S. Frassu, G. Viglialoro, Combining effects ensuring boundedness in an attraction a repulsion chemotaxis model with production and consumption, Z. Angew. Math. Phys., 74 (2023), 109–121
-
[26]
T. Li, N. Pintus, G. Viglialoro, Properties of solutions to porous medium problems with different sources and boundary conditions, Z. Angew. Math. Phys., 70 (2019), 18 pages
-
[27]
T. Li, Y. V. Rogovchenko, Oscillation of second-order neutral differential equations, Math. Nachr., 288 (2015), 1150–1162
-
[28]
T. Li, Y. V. Rogovchenko, Oscillation criteria for second-order superlinear Emden a Fowler neutral differential equations, Monatsh. Math., 184 (2017), 489–500
-
[29]
T. Li, Y. V. Rogovchenko, On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations, Appl. Math. Lett., 105 (2020), 7 pages
-
[30]
T. Li, G. Viglialoro, Boundedness for a nonlocal reaction chemotaxis model even in the attraction-dominated regime, Differential Integral Equations, 34 (2021), 315–336
-
[31]
F. Masood, O. Moaaz, S. S. Santra, U. Fernandez-Gamiz, H. A. El-Metwally, Oscillation theorems for fourth-order quasi-linear delay differential equations, AIMS Math., 8 (2023), 16291–16307
-
[32]
F. Masood, O. Moaaz, S. S. Santra, U. Fernandez-Gamiz, H. El-Metwally, On the monotonic properties and oscillatory behavior of solutions of neutral differential equations, Demonstr. Math., 56 (2023), 23 pages
-
[33]
M. Meganathan, S. S. Santra, L. A. Jayanathan, D. Baleanu, Numerical analysis of fractional order discrete Bloch equations, J. Math. Comput. Sci., 32 (2023), 222–228
-
[34]
O. Moaaz, E. M. Elabbasy, A. Muhib, Oscillation criteria for even-order neutral differential equations with distributed deviating arguments, Adv. Difference Equ., 2019 (2019), 10 pages
-
[35]
O. Moaaz, A. Muhib, T. Abdeljawad, S. S. Santra, M. Anis, Asymptotic behavior of even-order noncanonical neutral differential equations, Demonstr. Math., 52 (2022), 28–39
-
[36]
A. Ndiaye, F. Mansal, Existence and Uniqueness Results of Volterra-Fredholm Integro-Differential Equations via Caputo Fractional Derivative, J. Math., 2021 (2021), 8 pages
-
[37]
P. Raghavendran, T. Gunasekar, H. Balasundaram, S. S. Santra, D. Majumder, D. Baleanu, Solving fractional integrodifferential equations by Aboodh transform, J. Math. Comput. Sci., 32 (2024), 229–240
-
[38]
D. L. Russell, Controllability and stabilizability theory for linear partial differential equations: recent progress and open questions, SIAM Rev., 20 (1978), 639–739
-
[39]
S. Sangeetha, S. K. Thamilvanan, S. S. Santra, S. Noeiaghdam, M. Abdollahzadeh, Property A of third-order noncanonical functional differential equations with positive and negative terms, AIMS Math., 8 (2023), 14167–14179
-
[40]
S. S. Santra, Oscillation Criteria for Nonlinear Neutral Differential Equations of First Order with Several Delays, Mathematica, 57 (2015), 75–89
-
[41]
S. S. Santra, Necessary and sufficient conditions for oscillation of second-order differential equation with several delays, Stud. Univ. Babes¸-Bolyai Math., 68 (2023), 319–330
-
[42]
S. S. Santra, P. Mondal, M. E. Samei, H. Alotaibi, M. Altanji, T. Botmart, Study on the oscillation of solution to second-order impulsive systems, AIMS Math., 8 (2023), 22237–22255
-
[43]
S. S. Santra, S. Priyadharshini, V. Sadhasivam, J. Kavitha, U. Fernandez-Gamiz, S. Noeiaghdam, K. M. Khedher, On the oscillation of a certain class of conformable Emden-Fowler type elliptic partial differential equations, AIMS Math., 8 (2023), 12622–12636
-
[44]
S. S. Santra, A. Scapellato, Necessary and sufficient conditions for the oscillation of second-order differential equations with mixed several delays, J. Fixed Point Theory Appl., 24 (2022), 1–11
-
[45]
D. R. Smart, Fixed Point Theorems, Cup Archive, (1980)
-
[46]
A. Toma, O. Postavaru, A numerical method to solve fractional Fredholm-Volterra integro-differential equations, Alex. Eng. J., 68 (2023), 469–478
-
[47]
A. K. Tripathy, S. S. Santra, Necessary and sufficient conditions for oscillations to a second-order neutral differential equations with impulses, Kragujevac J. Math., 47 (2023), 81–93
-
[48]
X. Wang, L. Wang, Q. Zeng, Fractional differential equations with integral boundary conditions, J. Nonlinear Sci. Appl., 8 (2015), 309–314
-
[49]
J. Wu, Y. Liu, Existence and uniqueness of solutions for the fractional integro-differential equations in Banach spaces, Electron. J. Differential Equations, 2009 (2009), 1–8
-
[50]
Y. Zhou, J. Wang, L. Zhang, Basic theory of fractional differential equations, World Scientific Publishing Co., Hackensack, NJ (2017)