Solutions of boundary value problems for loaded hyperbolic type equations
This paper investigates a class of second-order partial differential equations describing wave processes with nonlocal effects, including cases involving fractional derivatives. Such equations often arise in the theory of elasticity, aerodynamics, acoustics, and electrodynamics. The presented equat...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2025-06-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
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| Online Access: | https://mts.buketov.edu.kz/index.php/mathematics-vestnik/article/view/945 |
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| author | N.T. Orumbayeva M.T. Kosmakova T.D. Tokmagambetova A.M. Manat |
| author_facet | N.T. Orumbayeva M.T. Kosmakova T.D. Tokmagambetova A.M. Manat |
| author_sort | N.T. Orumbayeva |
| collection | DOAJ |
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This paper investigates a class of second-order partial differential equations describing wave processes with nonlocal effects, including cases involving fractional derivatives. Such equations often arise in the theory of elasticity, aerodynamics, acoustics, and electrodynamics. The presented equations include both integral and differential terms, evaluated either at a fixed point x = x0 or x = α(t). An equation with a fractional derivative of order 0 ≤ β < 1 is considered, making it possible to model memory effects and other nonlocal properties. For each equation, supplemented by initial conditions, either a closed-form analytical solution is obtained or the main steps of its derivation are outlined. The article employs the Laplace transform to solve the resulting integral equation, enabling the solution to be presented in an explicit form.
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| format | Article |
| id | doaj-art-30fcd70c35754e4692bbbbfd6edc341e |
| institution | OA Journals |
| issn | 2518-7929 2663-5011 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj-art-30fcd70c35754e4692bbbbfd6edc341e2025-08-20T02:37:41ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112025-06-01118210.31489/2025m2/177-188Solutions of boundary value problems for loaded hyperbolic type equationsN.T. Orumbayeva0https://orcid.org/0000-0003-1714-6850M.T. Kosmakova1https://orcid.org/0000-0003-4070-0215T.D. Tokmagambetova2https://orcid.org/0000-0003-1984-8485A.M. Manat3https://orcid.org/0009-0008-5829-2786Karaganda Buketov University, Institute of Applied Mathematics, Karaganda, KazakhstanKaraganda Buketov University, Institute of Applied Mathematics, Karaganda, KazakhstanKaraganda Buketov University, Institute of Applied Mathematics, Karaganda, KazakhstanKaraganda Buketov University, Institute of Applied Mathematics, Karaganda, Kazakhstan This paper investigates a class of second-order partial differential equations describing wave processes with nonlocal effects, including cases involving fractional derivatives. Such equations often arise in the theory of elasticity, aerodynamics, acoustics, and electrodynamics. The presented equations include both integral and differential terms, evaluated either at a fixed point x = x0 or x = α(t). An equation with a fractional derivative of order 0 ≤ β < 1 is considered, making it possible to model memory effects and other nonlocal properties. For each equation, supplemented by initial conditions, either a closed-form analytical solution is obtained or the main steps of its derivation are outlined. The article employs the Laplace transform to solve the resulting integral equation, enabling the solution to be presented in an explicit form. https://mts.buketov.edu.kz/index.php/mathematics-vestnik/article/view/945differential equationspartial derivativesloaded equations boundary value problem Laplace transformconvolution |
| spellingShingle | N.T. Orumbayeva M.T. Kosmakova T.D. Tokmagambetova A.M. Manat Solutions of boundary value problems for loaded hyperbolic type equations Қарағанды университетінің хабаршысы. Математика сериясы differential equations partial derivatives loaded equations boundary value problem Laplace transform convolution |
| title | Solutions of boundary value problems for loaded hyperbolic type equations |
| title_full | Solutions of boundary value problems for loaded hyperbolic type equations |
| title_fullStr | Solutions of boundary value problems for loaded hyperbolic type equations |
| title_full_unstemmed | Solutions of boundary value problems for loaded hyperbolic type equations |
| title_short | Solutions of boundary value problems for loaded hyperbolic type equations |
| title_sort | solutions of boundary value problems for loaded hyperbolic type equations |
| topic | differential equations partial derivatives loaded equations boundary value problem Laplace transform convolution |
| url | https://mts.buketov.edu.kz/index.php/mathematics-vestnik/article/view/945 |
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