Function of Fractional Calculus and Relationship Between Distribution Theory and Partial Differential Equations

Shilpa Pal Shilpa; Chinta Mani Tiwari

doi:10.54060/a2zjournals.jase.64

Authors

Shilpa Pal Shilpa Department of Mathematics, Maharishi University of Information Technology, Lucknow, India
Chinta Mani Tiwari Department of Mathematics, Maharishi University of Information Technology, Lucknow, India

DOI:

https://doi.org/10.54060/a2zjournals.jase.64

Keywords:

Partial Differential Equations, Distribution theory, Burger's equation and Holmgren's theorem, Distributional Derivatives

Abstract

Partial Differential Equations are fundamental mathematical tools used to model physical phenomena across various disciplines such as physics, engineering, and economics. Solving PDEs often involves the concept of distributions, which extends the classical notion of functions to more generalized objects. This paper provides an introduction to PDEs, outlines the basic concepts of distribution theory, and discusses their interplay in solving PDEs. and distributional derivatives its convergence with distributional solution with space D^' (Ω) its extended form with weak derivatives.

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