This paper aims to handle some types of fractional differential equations with a fractional-order values β>1. In particular, we propose novel analytical solution called an atomic for certain linear type as well other partial exceeding one. Some examples are provided validate our findings.

Abstract In the present paper we utilize Proper Orthogonal Decomposition (POD) method for model order reduction in application to Smoluchowski aggregation equations with source and sink terms. particular, show practice that there exists a low-dimensional space allowing approximate solutions of equations. We also demonstrate it is possible process complexity depending only on dimension such but ...

LetG be a Hausdorff topological locally compact group. LetM(G) denote the Banach algebra of all complex and bounded measures on G. For all integers n ≥ 1 and all μ ∈ M(G), we consider the functional equations ∫ G f(xty)dμ(t) = ∑n i=1gi(x)hi(y), x,y ∈ G, where the functions f , {gi}, {hi}: G → C to be determined are bounded and continuous functions on G. We show how the solutions of these equati...

Various connections between 2-D gravity and KdV, dKdV, inverse scattering, etc. are established. For KP we show how to extract from the dispersionless limit of the Fay differential identity of Takasaki-Takebe the collection of differential equations for F = log(τ ) which play the role of Hirota type equations in the dispersionless theory. 1. HIROTA EQUATIONS In [7] we showed how second derivati...