A Note on F Transformation of Generalized Functions

Abstract

In this article we consider a new transformation named as F b a transformation. The distributional F b a transformation of compact support is defined as an analytic distribution. Two spaces of boehmians are also constructed. The generalized F b a transformation of a Boehmian is viewed as another Boehmian. Various properties of this transform are obtained in the generalized sense.

Results Involving Partial Differential Equations and Their Solution by Certain Integral Transform

“…In the sequel, extensions of double transformations are extensively developed for solving PDEs and obtaining results by performing solutions based on numerical approaches [20]. Double transforms such as the double Laplace transform [21][22][23], double Shehu transform [24], double Kamal transform [25], double Sumudu transform [26][27][28][29][30][31], double Elzaki transform [32], double Laplace-Sumudu transform [33][34][35] and ARA-Sumudu transform [36,37] have been considered in the literature. The ARA transform [15] was used for solving ordinary fractional differential equations [38] and some nonlinear PDEs [39].…”

Abelian and representation theorem for generalized Sumudu transform

“…The exhaustive literature survey revels that many authors have contributed their work in the extension of Sumudu transform to a generalized function and Bohemians. In [14,20] we can have generalized Sumudu transform and its fundamental properties. In [9] authors have proved the characterization theorem for generalized Natural transform.…”