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Fractal Sumudu Transform and Economic Models

Krishna Mani Nath, Bipan Hazarika, Hemanta Kalita

Abstract

In this paper, we present a new fractal derivative with a nonsingular kernel and analyze its fundamental properties. The effectiveness of the proposed operator is illustrated through the study of economic models using both the Caputo fractal derivative and the new fractal derivative.

Fractal Sumudu Transform and Economic Models

Abstract

In this paper, we present a new fractal derivative with a nonsingular kernel and analyze its fundamental properties. The effectiveness of the proposed operator is illustrated through the study of economic models using both the Caputo fractal derivative and the new fractal derivative.
Paper Structure (9 sections, 11 theorems, 66 equations)

This paper contains 9 sections, 11 theorems, 66 equations.

Table of Contents

  1. Introduction
  2. Preliminaries to Fractal Calculus
  3. Sumudu Transform
  4. Sumudu transform for some non-local fractal derivatives
  5. Main results
  6. A new fractal derivative without singular kernel
  7. Economic model formulated via the Caputo fractal derivative
  8. Economic model formulated via the wsk-fractal derivative
  9. Conclusions

Key Result

Theorem 2.10

Ali2 If the Sumudu transform of $f(t)$ is $\mathscr{S}(v)$, then the Sumudu transform of $D_F^\alpha f(t)$ is

Theorems & Definitions (40)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Definition 2.5
  • Example 2.6
  • Example 2.7
  • Definition 2.8: The fractal Sumudu transform
  • Example 2.9
  • Theorem 2.10
  • ...and 30 more