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Volume 60 >>> № 5 SEPTEMBER — OCTOBER 2024

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UDC 517.95

E.T. Karimov¹, N.E. Tokmagambetov², D.A. Usmonov³

¹ Fergana State University, Fergana, Uzbekistan

² Centre de Recerca Matematica Cerdanyola del Valles, Barcelona, Spain, and Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

tokmagambetov@crm.cat; tokmagambetov@math.kz

³ Fergana State University, Fergana, Uzbekistan

dusmonov909@gmail.com

INVERSE-INITIAL PROBLEM FOR TIME-DEGENERATE PDE
INVOLVING THE BI-ORDINAL HILFER DERIVATIVE

Abstract. A unique solvability of the inverse initial problem for a time-degenerate fractional partial differential equation is proved. Using the method of variable separation, we obtain the Cauchy problem for the fractional differential equation involving the bi-ordinal Hilfer derivative in the time variable. The authors present the solution to this Cauchy problem in an explicit form via the Kilbas–Saigo function. Further, using the upper and lower bounds of this function, the authors prove the uniform convergence of the infinite series corresponding to the solution of the formulated inverse initial problem.

Keywords: inverse-initial problem, degenerate PDE, bi-ordinal Hilfer operator, Kilbas–Saigo function.

full text

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UDC 517.95

INVERSE-INITIAL PROBLEM FOR TIME-DEGENERATE PDE INVOLVING THE BI-ORDINAL HILFER DERIVATIVE

REFERENCES

INVERSE-INITIAL PROBLEM FOR TIME-DEGENERATE PDE
INVOLVING THE BI-ORDINAL HILFER DERIVATIVE