VAQT BOʻYICHA KASR TARTIBLI TOʻLQIN TENGLAMASI UCHUN BIR NOLOKAL MASALA HAQIDA

Authors

  • Alimov Z
  • Olloyarov M

Keywords:

Xilfer kasr tartibli hosilasi; toʻlqin tenglamasi; Koshi masalasi; Furye usuli

Abstract

Ushbu maqolada vaqt oʻzgaruvchisi boʻyicha umumlashgan Xilfer kasr tartibli operatori ishtirok etgan toʻlqin tenglamasi uchun nolokal shartli chegaraviy masalaning bir qiymatli yechilishi tadqiq etilgan. Bunda oʻzgaruvchilarni ajratish usuli hamda kasr tartibli tenglama uchun Koshi masalasini yechish usullaridan foydalanilgan.

References

Courant, R., Hilbert, D. (1962). Methods of Mathematical Physics, vol. II, New York: Wiley-Interscience.

Gershenfeld, N. (1999). The Nature of Mathematical Modeling (1st ed.), New York: Cambridge University Press.

Wazwaz, Abdul-Majid (2009). Partial Differential Equations and Solitary Waves Theory. Higher Education Press.

Roubíček, T. (2013). Nonlinear Partial Differential Equations with Applications. International Series of Numerical Mathematics, vol. 153 (2nd ed.), Basel, Boston, Berlin: Birkhäuser.

Uchaikin V.V. (2013). Fractional Derivatives for Physicists and Engineers. Vol.1. Background and Theory. Springer, Berlin, Heidelberg.

Uchaikin V.V. (2013). Fractional Derivatives for Physicists and Engineers. Vol.2. Applications. Springer, Berlin, Heidelberg.

Kilbas A.A., Srivastava H.M., Trujillo J.J. (2006). Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam.

Podlubny I. (1999). Fractional Differential Equations. Academic Press, San Diego.

Nigmatullin R.R. (1984). On the theory of relaxation with “remnant” memory. Phys. Status Solidi B, 124(1), pp.389-393.

De Oliveira, E.C.; Tenreiro Machado, J.A. (2014). A review of definitions for fractional derivatives and integral. Math. Probl. Eng., 238459.

Bulavatsky V.M. (2014). Closed form of the solutions of some boundary problems for anomalous diffusion equation with Hilfer’s generalized derivative. Cybernetics and Systems Analysis. 30(4), pp. 570-577.

Dzhrbashyan M. M., Nersesyan A. B. (1968). Fractional Derivatives and the Cauchy Problem for Fractional Differential Equations, Izv. Akad. Nauk Armyan. SSR. 3, No 1 (1968), 3-29.

Alimov Z. S. (2022). On a boundary-value problem for the degenerate wave equation in a prismatic domain. Bull. Inst. Math., Vol. 5, No3, pp. 36-40.

David J., Nolte A., Sherman J. (2018). A Boundary-Value Problem for 3-D Fractional Wave Equation with Singularity. Bull. Inst. Math., Vol. 1, No2, pp. 28-52.

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Published

2023-02-16

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