Thursday 06 March 2025
Researchers have made significant progress in solving complex mathematical problems related to fractional order systems, which describe phenomena that exhibit non-integer behavior. These systems are crucial for understanding various natural and artificial processes, such as heat transfer, vibrations, and signal processing.
One of the primary challenges in dealing with these systems is finding efficient methods to solve the corresponding equations. The Adomian decomposition method has been a popular approach in recent years, as it allows researchers to break down complex problems into simpler components that can be solved independently.
In this study, scientists employed a novel combination of techniques to tackle nonlinear fractional order systems. They used the Aboodh transform to simplify the fractional derivatives and then applied the Adomian decomposition method to obtain the solution. This approach proved to be highly effective in solving a range of problems related to thermoelasticity, which is the study of how heat and mechanical stresses interact.
Thermoelasticity plays a vital role in understanding various phenomena, such as thermal conductivity, stress, elasticity, and temperature interactions. The researchers’ findings have significant implications for fields like materials science, engineering, and physics.
The study’s results show that the proposed method can accurately solve nonlinear fractional order systems with high precision. This is particularly important in fields where small errors can have significant consequences, such as in the design of new materials or devices.
The scientists also investigated the behavior of the solutions at different fractional orders. They found that as the fractional orders approach integer values, the solutions converge to those obtained using traditional methods. This suggests that the proposed method can be used as a bridge between classical and fractional order systems.
The researchers’ work has opened up new avenues for exploring complex phenomena in various fields. Their innovative approach offers a powerful tool for solving nonlinear fractional order systems, which will likely have far-reaching implications for science and technology.
By combining the Aboodh transform with the Adomian decomposition method, scientists can tackle even more challenging problems related to fractional order systems. This breakthrough has the potential to revolutionize our understanding of complex phenomena and lead to the development of new technologies and materials.
Cite this article: “Unlocking Complex Phenomena: A Novel Approach to Solving Nonlinear Fractional Order Systems”, The Science Archive, 2025.
Fractional Order Systems, Nonlinear Problems, Adomian Decomposition Method, Aboodh Transform, Thermoelasticity, Materials Science, Engineering, Physics, Heat Transfer, Signal Processing.
