Fractional Derivative of Hyperbolic Function
DOI:
https://doi.org/10.20956/j.v21i1.35860Keywords:
Maclaurin series, hyperbolic function, fractional derivativeAbstract
Fractional derivative is a generalization of ordinary derivative with non-integer or fractional order. This research presented fractional derivative of hyperbolic function (hyperbolic sine, hyperbolic cosine, hyperbolic tangent, hyperbolic cotangent, hyperbolic secant, and hyperbolic cosecant) with order constraint . The hyperbolic function is presented in Maclaurin series form. Then, the fractional derivative can be determined by using definition of Riemann-Liouville fractional derivative. The result is simulated by using Matlab softwareDownloads
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DAFTAR PUSTAKA
Alquran, M., 2023. The Amazing Fractional Maclaurin Series for Solving Different Types of Fractional Mathematical Problems that Arise in Physics and Engineering. Partial Differential Equations in Applied Mathematics, 7, 100506. https://doi.org/10.1016/j.padiff.2023.100506
Banerjee, J., Ghosh, U., Sarkar, S., & Das, S., 2017. A Study of Fractional Schrödinger Equation Composed of Jumarie Fractional Derivative. Pramana, 88(4), 70. https://doi.org/10.1007/s12043-017-1368-1
Daraghmeh, A., Qatanani, N., & Saadeh, A., 2020. Numerical Solution of Fractional Differential Equations. Applied Mathematics, 11(11), 1100–1115. https://doi.org/10.4236/am.2020.1111074
Das, S., 2011. Functional Fractional Calculus (Vol. 1). Springer.
Gatzke, E., 2021. Introduction to MATLAB. In Introduction to Modeling and Numerical Methods for Biomedical and Chemical Engineers (pp. 99–121). Springer.
Hilfer, R., Luchko, Y., & Tomovski, Z., 2009. Operational Method for The Solution of Fractional Differential Equations with Generalized Riemann-Liouville Fractional Derivatives. Fract. Calc. Appl. Anal, 12(3), 299–318.
Miller, K. S., & Ross, B., 1993. An Introduction to The Fractional Calculus and Fractional Differential Equations. John Wiley, Inc.
Petráš, I., 2011. Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation. Springer Science & Business Media.
Podlubny, I., 1999. Fractional Differential Equations, Mathematics in Science and Engineering. Academic press New York.
Stewart, J., Clegg, D., & Watson, S., 2021. Calculus: Early Transcendentals. Cengage Learning.
Yang, X.-J., Gao, F., & Ju, Y., 2020. General Fractional Derivatives with Applications in Viscoelasticity. Academic Press.
Zhang, T., Yang, Z.-H., Qi, F., & Du, W.-S., 2024. Some Properties of Normalized Tails of Maclaurin Power Series Expansions of Sine and Cosine. Fractal and Fractional, 8(5), 257. https://doi.org/10.3390/fractalfract8050257
Zhou, Y., 2024. Basic Theory of Fractional Differential Equations Third Edition. World Scientific Publishing.
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