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The purpose of this paper is to solve a kind of the Riemann–Hilbert boundary value problem for(φ,ψ){(\varphi,\psi)}-harmonic functions, which are linked with the use of two orthogonal bases of the Euclidean spaceℝm{\mathbb{R}^{m}}. We approach this problem using the language of Clifford analysis for obtaining an explicit expression of the solution of the problem in a Jordan domainΩ⊂ℝm{\Omega\subset\mathbb{R}^{m}}with fractal boundary. Since our study is concerned with a second order differential operator, the boundary data are restricted to involve the higher order Lipschitz classLip⁡(1+α,Γ){\operatorname{Lip}(1+\alpha,\Gamma)}.

On a Riemann--Hilbert boundary value problem for (ϕ,ψ)-harmonic functions in ℝ m