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INTEGRO-DIFFERENTIAL EQUATIONS EMBODYING POWERS OF A DIFFERENTIAL OPERATOR
- Authors: Parasidis I.N.1, Providas E.2
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Affiliations:
- University of Thessaly, Greece
- University of Thessaly, Greece
- Issue: Vol 25, No 3 (2019)
- Pages: 12-21
- Section: Articles
- URL: https://journals.ssau.ru/est/article/view/7651
- DOI: https://doi.org/10.18287/2541-7525-2019-25-3-12-21
- ID: 7651
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Abstract
We establish solvability and correctness criteria for two Fredholm type linear integro-differential operators B2, B4 encompassing up to second and fourth powers, respectively, of a differential operator A� with aknown inverse I = A�−1. We also derive explicit solution formulae to corresponding initial and boundary value problems by using the inverse of the differential operator. The approach is based on the theory of the extensions of linear operators in Banach spaces. Three example problems for ordinary and partial integro-differential operators are solved.
About the authors
I. N. Parasidis
University of Thessaly,Greece
Email: morenov@ssau.ru
ORCID iD: 0000-0002-7900-9256
Сandidate of Technical Sciences, associate professor
E. Providas
University of Thessaly,Greece
Author for correspondence.
Email: morenov@ssau.ru
ORCID iD: 0000-0002-0675-4351
Сandidate of Technical Sciences, associate professor
References
- Biyarov B.N., Abdrasheva G.K. Relatively Bounded Perturbations of Correct Restrictions and Extensions of Linear Operators. Functional Analysis in Interdisciplinary Applications. FAIA 2017. Springer Proceedings in Mathematics & Statistics. Springer, 2017, issue 216, pp. 213–221. doi: 10.1007/978-3-319-67053-9 .
- Parasidis I.N., Providas E. Extension Operator Method for the Exact Solution of Integro-Differential Equations.In: Contributions in Mathematics and Engineering: In Honor of Constantin Carath´eodory. Cham, SpringerInternational Publishing, 2016, pp. 473–496. doi: 10.1007/978-3-319-31317-7 .
- Parasidis I.N., Providas E. Resolvent Operators for Some Classes of Integro-Differential Equations.In: Mathematical Analysis, Approximation Theory and Their Applications. Cham, Springer InternationalPublishing, 2016, pp. 535–558. doi: 10.1007/978-3-319-31281-1 .
- Parasidis I.N., Providas E. On the Exact Solution of Nonlinear Integro-Differential Equations. In: Applications of Nonlinear Analysis. Cham, Springer International Publishing, 2018, pp. 591–609. doi: 10.1007/978-3-319-89815-5 .
- Polyanin A.D., Manzhirov A.V. Handbook of integral equations. Boca Raton, Florida, USA: CRC Press LLC, 1998 .
- Polyanin A.D., Zhurov A.I. Exact solutions to some classes of nonlinear integral, integro-functional, and integro-differential equations. Dokl. Math., 2008, issue 77, pp. 315–319. doi: 10.1134/S1064562408020403 .
- Vassiliev N.N., Parasidis I.N., Providas E. Exact solution method for Fredholm integro-differential equations with multipoint and integral boundary conditions. Part 1. Extention method. Information and Control Systems, 2018, issue 6, pp. 14–23. doi: 10.31799/1684-8853-2018-6-14-23 .
- Vassiliev N.N., Parasidis I.N., Providas E. Exact solution method for Fredholm integro-differential equations with multipoint and integral boundary conditions. Part 2. Decomposition-extension method for squared operators. Information and Control Systems, 2019, issue 2, pp. 2–9. doi: 10.31799/1684-8853-2019-2-2-9 .
- Wazwaz A.M. Linear and nonlinear integral equations, methods and applications. Berlin, Heidelberg: Springer, 2011. doi: 10.1007/978-3-642-21449-3 .
- Zhu X., Li L. Closed form solution for a nonlocal strain gradient rod in tension. Int. J. Eng. Sci., 2017, issue 119, pp. 16–28. doi: 10.1016/j.ijengsci.2017.06.019 .
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