We establish one-body reduced density matrix (1RDM) functional theory for the canonical ensemble in a finite basis set at an elevated temperature. Including temperature guarantees differentiability of universal by occupying all states and additionally not fully fermionic system. use convexity invertibility potential-to-1RDM map to show that subgradient contains only one element which is equival...

In this paper a numerical method for solving second order fuzzy differential equations under generalized differentiability is proposed. This method is based on the interpolating a solution by piecewise polynomial of degree 4 in the range of solution. Moreover we investigate the existence, uniqueness and convergence of approximate solutions. Finally the accuracy of piecewise approximate method b...

In this paper we intend to offer new numerical methods to solve the second-order fuzzy Abel-Volterraintegro-differential equations under the generalized $H$-differentiability. The existence and uniqueness of thesolution and convergence of the proposed methods are proved in details and the efficiency of the methods is illustrated through a numerical example.

In this paper,  The Picard method is proposed to solve the system of first-order fuzzy  differential equations  $(FDEs)$ with fuzzy initial conditions under generalized $H$-differentiability. Theexistence and uniqueness of the solution and convergence of theproposed method are proved in details. Finally, the method is illustrated by solving some examples.