Geodesic
On the solution of some higher-order integro-differential equations of special form
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 26 (2020) no. 1, pp. 14-22 Cet article a éte moissonné depuis la source Math-Net.Ru

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The article is devoted to the solution of boundary value problems for higher-order linear integro-differential equations of Fredholm type with differential and integral operators encompassing powers of an ideal bijective linear differential operator whose inverse is known explicitly. The conditions for existence and uniqueness of solutions are derived and the solutions are delivered in closed form. The approach is based on the view that an integro-differential operator is a perturbed differential operator. The results obtained are of both theoretical and practical importance. The method is elucidated by solving two illustrative problems.
Keywords: integro-differential equations, initial value problems, boundary value problems, differential operators, power operators, composite products
Mots-clés : exact solutions. 
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E. Providas; I. N. Parasidis. On the solution of some higher-order integro-differential equations of special form. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 26 (2020) no. 1, pp. 14-22. http://geodesic.mathdoc.fr/item/VSGU_2020_26_1_a1/

[1] F. Bloom, “Ill posed Problems for Integrodifferential Equations in Mechanics and Electromagnetic Theory”, SIAM, 1981, 101–154 | DOI | MR

[2] A. Hirsa, S. N. Neftci, An Introduction to the Mathematics of Financial Derivatives, Academic Press, Cambridge, 2013 | DOI | MR | Zbl

[3] N. A. Kil'chevski, “Integrodifferential and integral equations of equilibrium of thin elastic shells”, PMM, 23:1 (1959), 124–133 | Zbl

[4] J. Medlock, M. Kot, “Spreading disease: integro-differential equations old and new”, Math. Biosci., 184 (2003), 201–222 | DOI | MR | Zbl

[5] R. P. Agarwal, “Boundary value problems for higher order integro-differential equations”, Nonlinear Analysis-theory Methods Applications, 7:3 (1983), 259–270 | DOI | MR | Zbl

[6] E. Aruchunan, Y. Wu, B. Wiwatanapataphee, P. Jitsangiam, “A New Variant of Arithmetic Mean Iterative Method for Fourth Order Integro-differential Equations Solution”, 2015 3rd International Conference on Artificial Intelligence, Modelling and Simulation (AIMS) (Kota Kinabalu, 2015), 82–87 | DOI

[7] T. K. Yuldashev, “An inverse problem for a nonlinear Fredholm integro-differential equation of fourth order with degenerate kernel”, J. Samara State Tech. Univ., Ser. Phys. Math. Sci., 19:4 (2015), 736–749 (In Russ.) | DOI | MR | Zbl

[8] K. Atkinson, The Numerical Solution of Integral Equations of Second Kind, Cambridge University Press, Cambridge, 1997 | DOI | MR | Zbl

[9] A. M. Wazwaz, Linear and nonlinear integral equations, methods and applications, Springer, Berlin–Heidelberg, 2011 | DOI | MR | Zbl

[10] A. D. Polyanin, A. V. Manzhirov, Handbook of integral equations, CRC Press LLC, Boca Raton, Florida, USA, 1998 http://inis.jinr.ru/sl/M_Mathematics/MC_Calculus/MCde_Differential equations/Polyanin, Manzhirov. Handbook of integral equations (CRC, 1998)(796s).pdf | MR | Zbl

[11] A. D. Polyanin, A. I. Zhurov, “Exact solutions to some classes of nonlinear integral, integro-functional, and integro-differential equations”, Doklady Mathematics, 77 (2008), 315–319 | DOI | MR

[12] M. Rahman, Integral Equations and their Applications, WIT Press, Southhampton–Boston, 2007, 355 pp. | DOI | MR | Zbl

[13] B. N. Biyarov, “Normal extensions of linear operators”, Eurasian Math. J., 7:3 (2016), 17–32 | MR | Zbl

[14] B. K. Kokebayev, M. Otelbaev, A. N. Shynybekov, “On questions of extension and restriction of operators”, Dokl. Akad. Nauk SSSR, 271:6 (1983), 1307–1310 (In Russ.) | MR

[15] R. O. Oinarov, I. N. Parasidis, “Correct extensions of operators with finite defect in Banach spaces”, Izv. Akad. Kaz. SSR, 1988, no. 5, 42–46 (In Russ.) | MR | Zbl

[16] M. M. Baiburin, E. Providas, “Exact Solution to Systems of Linear First-Order Integro-Differential Equations with Multipoint and Integral Conditions”, Mathematical Analysis and Applications, Springer Optimization and Its Applications, 154, Springer, Cham, 2019, 1–16 | DOI | Zbl

[17] I. N. Parasidis, E. Providas, “Extension Operator Method for the Exact Solution of Integro-Differential Equations”, Contributions in Mathematics and Engineering, In Honor of Constantin Carathéodory, Springer International Publishing, Cham, 2016, 473–496 | DOI | MR | Zbl

[18] I. N. Parasidis, E. Providas, “Resolvent Operators for Some Classes of Integro-Differential Equations”, Mathematical Analysis, Approximation Theory and Their Applications, Springer International Publishing, Cham, 2016, 535–558 | DOI | MR | Zbl

[19] I. N. Parasidis, E. Providas, “Integro-differential equations embodying powers of a differential operator”, Vestnik of Samara University. Natural Science Series, 25:3 (2019), 12–21 (In Russ.) | DOI | MR | Zbl

[20] N. N. Vassiliev, I. N. Parasidis, E. Providas, “Exact solution method for Fredholm integro-differential equations with multipoint and integral boundary conditions. Part 1. Extention method”, Information and Control Systems, 2018, no. 6, 14–23 | DOI

[21] N. N. Vassiliev, I. N. Parasidis, E. Providas, “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, no. 2, 2–9 | DOI | MR