This paper provides a description of an algebraic setting for the Lagrangian formalism over graded algebras and is intended as the necessary first step towards the noncommutative C-spectral sequence (variational bicomplex). A noncommutative version of integration procedure, the notion of adjoint operator, Green’s formula, the relation between integral and differential forms, conservation laws, ...

This paper provides a description of an algebraic setting for the Lagrangian formalism over graded algebras and is intended as the necessary rst step towards the noncommutative C-spectral sequence (variational bicomplex). A noncommutative version of integration procedure, the notion of adjoint operator, Green's formula, the connection between integral and di erential forms, conservation laws, E...

In this paper, we introduce the concept of bicomplex-valued controlled metric spaces and prove fixed point theorems. Our results mainly focus on generalizing expanding some recently established results. Finally, explain an application our main result to a certain type fractional differential equation.

With the increasing importance of Mittag-Leffler function in physical applications, these days many researchers are studying various generalizations and extensions function. In this paper efforts made to define bicomplex extension also its analyticity region convergence discussed. Various properties including integral representation, recurrence relations, duplication formula differential relati...

Given a Lie group acting on a manifold, our aim is to analyze the evolution of differential invariants under invariant submanifold flows. The constructions are based on the equivariant method of moving frames and the induced invariant variational bicomplex. Applications to integrable soliton dynamics, and to the evolution of differential invariant signatures, used in equivalence problems and ob...

In this work we show that the systems of balance equations (balance systems) of continuum thermodynamics occupy a natural place in the variational bicomplex formalism. We apply the vertical homotopy decomposition to get a local splitting (in a convenient domain) of a general balance system as the sum of a Lagrangian part and a complemental “pure non-Lagrangian” balance system. In the case when ...

Abstract In this paper we present parallel theories on constructing Wiener algebras in the bicomplex setting. With appropriate symmetry condition, matrix valued case can be seen as a complex and, case, make necessary connection between analysis and with symmetry. We also write an application to superoscillations case.