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@article{179341,
        author = {R. S. Pawar and Dr. A. N. Rangari and V. D. Sharma},
        title = {Testing Function Spaces and Operation Transform Formulae for Sumudu-Laplace Transform},
        journal = {International Journal of Innovative Research in Technology},
        year = {2025},
        volume = {11},
        number = {12},
        pages = {6810-6817},
        issn = {2349-6002},
        url = {https://ijirt.org/article?manuscript=179341},
        abstract = {Integral transforms are a critical class of mathematical techniques used to simplify and solve complex problems in a wide range of engineering and scientific disciplines. The Laplace Transform, which converts differential equations into algebraic equations in the complex frequency domain, is especially useful for solving initial value problems (IVPs). It is widely used in control theory, signal processing, electronics, and mechanical systems, where systems are modeled by ordinary differential equations (ODEs). This transform is particularly effective for analyzing the behavior of dynamic systems, such as electrical circuits, vibrations, and systems governed by transient conditions.
The Sumudu Transform is an emerging alternative that, like the Laplace transform, can convert complex differential equations into simpler forms for easier solving. However, it offers distinct advantages in certain problem scenarios: Effective for Boundary Value Problems, Applications in Control Theory and Electrical Engineering, Efficiency in Numerical solutions.
The present paper gives the various testing function spaces which are the backbone of distribution theory. And by using these testing function spaces we have described the operation transform formulae of Sumudu-Laplace transform which will be useful for solving various differential and integral equations.},
        keywords = {Differential operator, Generalized function, Laplace Transform, shifting & Scaling Property, Sumudu Transform, Sumudu-Laplace Transform, Testing function space},
        month = {May},
        }