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On the solutions of Cauchy problem for two classes of semi-linear pseudo-differential equations over \(p\)-adic field. (English) Zbl 07090162
Summary: Throughout this paper, using the \(p\)-adic wavelet basis together with the help of separation of variables and the Adomian decomposition method (as a scheme in numerical analysis) we initially investigate the solution of Cauchy problem for two classes of the first and second order of pseudo-differential equations involving the pseudo-differential operators such as Taibleson fractional operator in the setting of \(p\)-adic field.

65Lxx Numerical methods for ordinary differential equations
65-XX Numerical analysis
35Qxx Partial differential equations of mathematical physics and other areas of application
65Zxx Applications to the sciences
37-XX Dynamical systems and ergodic theory
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