an:07090162
Zbl 7090162
Pourhadi, Ehsan; Khrennikov, A. Yu.
On the solutions of Cauchy problem for two classes of semi-linear pseudo-differential equations over \(p\)-adic field
EN
\(p\)-Adic Numbers Ultrametric Anal. Appl. 10, No. 4, 322-343 (2018)
2070-0466 2070-0474
2018
j
65Lxx 65-XX 35Qxx 65Zxx 37-XX
Cauchy problem; pseudo-differential equations; \(p\)-adic field; \(p\)-adic wavelet basis; Adomian decomposition method; Abel Equation
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.