Gene

Initial value problem

Quantum mechanics

Transformation (genetics)

Convection–diffusion equation

Pure mathematics

Service (business)

Homotopy

Applied mathematics

Perturbation (astronomy)

Cauchy problem

Economics

Biochemistry

Physics

Mathematics

Homotopy analysis method

Transcription factor

Mathematical analysis

Cauchy distribution

Repressor

Economy

Chemistry

Diffusion equation

Operator (biology)

Fractional calculus

Homotopy perturbation method

Journal of Function Spaces

In this article, the new iterative transform technique and homotopy perturbation transform method are applied to calculate the fractional-order Cauchy-reaction diffusion equation solution. Yang transformation is mixed with the new iteration method and homotopy perturbation method in these methods. The fractional derivative is considered in the sense of Caputo-Fabrizio operator. The convection-diffusion models arise in physical phenomena in which energy, particles, or other physical properties are transferred within a physical process via two processes: diffusion and convection. Four problems are evaluated to demonstrate, show, and verify the present methods’ efficiency. The analytically obtained results by the present method suggest that the method is accurate and simple to implement.

Novel Investigation of Fractional-Order Cauchy-Reaction Diffusion Equation Involving Caputo-Fabrizio Operator