##plugins.themes.academic_pro.article.sidebar##

Download
pdf
Statistic
Read Counter : 11 Download : 22

##plugins.themes.academic_pro.article.main##

Abstract

This paper is devoted to the proof of the uniqueness and existence of a solution to a nonlocal
problem with an integral gluing condition for a loaded equation of parabolic-hyperbolic type, including
the Caputo operator of fractional order. The uniqueness of the problem posed is proved by the method of
energy integrals, and existence - by the method of integral equations

Keywords

Loaded equation, parabolic-hyperbolic type, fractional order operator in the sense of Caputo, integral gluing condition, uniqueness and existence of solution, integral equation of Volterra

##plugins.themes.academic_pro.article.details##

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite
Nafasov Ganisher Abdurashidovich, & Jamuratov Kengash. (2022). The Local Problem with Integral Gluing Condition for Loaded Mixed Type Equation Involving the Caputo Fractional Derivative. Texas Journal of Engineering and Technology, 14, 20–26. Retrieved from https://zienjournals.com/index.php/tjet/article/view/2845

References

  1. Kilbas A.A., Srivastava H.M., Trujillo J.J. Theory and Applications of Fractional Differential Equations, in: North-Holland Mathematics Studies, vol. 204, Amsterdam: Elsevier, 2006. 523 p.
  2. Miller K.S., Ross B. An Introduction to the Fractional Calculus and DifferentialEquations, John Wiley, New York. 1993.
  3. Podlubny I.. Fractional Differential Equations. Academic Press. New York. 1999. 364 p.
  4. Samko S.G., Kilbas A.A., Marichev O.I. Integrals and derivatives of fractional order and some of their applications. Minsk: Science and Technology. 1987.688 p.
  5. Pskhu A.V. Fractional partial differential equations. Moscow: Nauka, 2005.199 p.
  6. Kadirkulov B. J. Boundary problems for mixed parabolic-hyperbolic equations with two
  7. lines of changing type and fractional derivative. Electronic Journal of Differential Equations.
  8. 2014. 2014(57) . pp. 1–7.
  9. Karimov E. T., Akhatov J. A boundary problem with integral gluing condition for a
  10. parabolic-hyperbolic equation involving the Caputo fractional derivative. Electronic Journal
  11. of Differential Equations. 2014. 2014(14). pp. 1–6.
  12. Ashurov R.R., Cabada A., Turmetov B.Kh. Operator method for construction of solutions of linear fractional differential equations with constant coefficients. Fract. Calc. & Appl. Anal.Springer, 2016. 19(1). pp. 229-251.
  13. AbdullaevO. Kh., Islomov B. I. Gellerstedt Type Problem for the Loaded Parabolic-Hyperbolic
  14. Type Equation with Caputo and Erdelyi–Kober Operators of Fractional Order. Russian
  15. Mathematics. 2020. 64(10). pp. 29–42.
  16. Nakhushev A.M. Equations of Mathematical Biology. M .: Higher school, 1995. 301p.
  17. Nakhushev A.M. Loaded equations and their applications. M .: Science. 2012.233p.
  18. Kaziev V.M. Goursat problem for one loaded integro-differential equations. Differential. equations. 1981. T. 17. No 2. pp. 313–319.
  19. Islomov B.I, Kuryazov D. Boundary value problems for a loaded mixed equation type of the third order. Uzbek mathematical journal. 2000. No. 2. pp.29-35.
  20. Eleev V.A., Dzarahokhov A.V. A nonlocal boundary value problem for a loaded third order equations. Vladikavkaz mathematical journal. 2004.Vol. 6.
  21. Khubiev K.U. On a boundary value problem for a loaded equation of a mixed hyperbolic-parabolic type. Dokl. Adyg. (Circassian.) Intern. acad. sciences. 2005.
  22. B.Islomov, U. Baltaeva. Boudanry-value problems for a third-order loaded parabolic-hyperbolic
  23. type equation with variable coefficients. EJDE. 2015 (2015). No.221. pp 1-10.
  24. Ubaidullaev U.Sh. The inverse problem for a mixed loaded equation with the Riemann-Liouville operator in a rectangular region // Bulletin of KRAUNC. Phys.-mat.science. 2020.31 (2). pp.18-31
  25. Sabitov K. B., Melisheva E. P. The Dirichlet problem for a loaded mixed-typeequation in a
  26. rectangular domain, Russian Math. 2013. 57( 7). pp. 53-65.
  27. Sabitov K.B. An initial-boundary value problem for a parabolic-hyperbolic equation with
  28. loaded terms, Russian Math. 2015.59 (6). pp. 23-33.
  29. Ramazanov M.I. On a nonlocal problem for a loaded hyperbolic-elliptic equations in a rectangular domain. // Mat. magazine. Almaty. 2002.2 (4). pp. 75–81
  30. Islomov, B. I.; Yuldashev, T. K.; Ubaydullayev,U.Sh. On Boundary Value Problems for a Mixed
  31. Type Fractional Differential Equation with Caputo Operator. Bulletin of the Karaganda
  32. University. Mathematics series. 2021. 1(101). pp.127-137 .
  33. Salakhitdinov M.S., Karimov E.T. On a nonlocal problem with conjugation conditions of the integral form for the parabolic-hyperbolic one with the Caputo operator. Reports of the Academy of Sciences of the Republic of Uzbekistan. 2014. No. 4. pp.6-9.
  34. Abdullaev O.Kh. A nonlocal problem for a loaded mixed-type equation with integral operator. Vestnik Sam. state tech. university. Series of Physics and Mathematics. 2016.
  35. Smirnov M.M. Mixed type equations. M .: Higher school. 1985.304 p.
  36. Mikhlin S.G. Lectures on linear integral equations. M .: Fizmatgiz. 1959.232 p.