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How can the Caputo derivative be used to solve real world problems?

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Cubic Hermite spline

Biorthogonal system

Hermite polynomials

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The Caputo derivative can be used to solve real-world problems by providing efficient algorithms and numerical methods for solving fractional models and equations . It allows for the reduction of these problems to systems of algebraic equations, making them easier to solve. The Caputo derivative is used in various fields such as optimal control problems, cancer modeling, viral diseases modeling, and macroeconomic modeling. It provides stability results, graphical results, and closed-form solutions for these problems. Additionally, the Caputo derivative is used in the analysis of chaotic behavior, periodic and quasi-periodic limit cycles, and the study of the dynamics of various systems. Overall, the Caputo derivative offers a powerful tool for solving real-world problems in different domains.

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Open access•Journal Article•DOI Novel Fractional Models Compatible with Real World Problems Ramazan Ozarslan, Ahu Ercan, Erdal Bas - Show less +2 more 01 Apr 2019 17 Citations	The Caputo derivative can be used to solve real world problems by providing analytical solutions, as demonstrated in the paper.
Open access•Journal Article•DOI Analysis of Multiterm Initial Value Problems with Caputo–Fabrizio Derivative Mohammed Al-Refai, Muhammed I. Syam - Show less +1 more 13 Nov 2021-Journal of Mathematics	The Caputo derivative can be used to solve real-world problems by providing necessary and sufficient conditions for the existence of solutions and obtaining closed-form solutions.
Journal Article•DOI New numerical simulations for some real world problems with Atangana–Baleanu fractional derivative Wei Gao, Behzad Ghanbari, Behzad Ghanbari, Haci Mehmet Baskonus - Show less +3 more 01 Nov 2019-Chaos Solitons & Fractals 101 Citations	The Caputo derivative can be used to solve real world problems by providing a numerical method for solving fractional models, such as viral diseases and macroeconomic models.
Open access•Journal Article•DOI Application of Caputo-Fabrizio derivative to a cancer model with unknown parameters M. M. El-Dessoky, Muhammad Altaf Khan - Show less +1 more 01 Jan 2021 4 Citations	The Caputo derivative can be used to model and analyze the dynamics of real-world problems, such as cancer growth, by incorporating fractional order dynamics.
Journal Article•DOI Solving Fractional Optimal Control Problems Involving Caputo–Fabrizio Derivative Using Hermite Spline Functions Araz Noori Dalawi, Mehrdad Lakestani, Elmira Ashpazzadeh - Show less +2 more 08 Feb 2023	The Caputo derivative can be used to solve real-world problems by reducing them to systems of algebraic equations using operational matrices derived from Hermite cubic spline functions.

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