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Bifurcation analysis and novel wave patterns to Zakharov-Kuznetsov-Benjamin-Bona-Mahony equation with truncated M-fractional derivative. [PDF]

Sci Rep
Ahmad J, Masood K, Ayub F, Shah NA.
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Two compartmental fractional derivative model with general fractional derivative

Journal of Pharmacokinetics and Pharmacodynamics, 2022
This study presents a new two compartmental model with, recently defined General fractional derivative. We review that concept of General fractional derivative and use the kernel function that generalizes the classical Caputo derivative in a mathematically consistent way.
Vesna Miskovic-Stankovic, Marko Janev, Teodor M. Atanackovic   +2 more
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Discretised general fractional derivative

Mathematics and Computers in Simulation, 2023
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Enyu Fan, Changpin Li, Martin Stynes
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Fractional viscoelastic models with Caputo generalized fractional derivative

Mathematical Methods in the Applied Sciences, 2021
This article focuses on fractional Maxwell model of viscoelastic materials, which are a generalization of classic Maxwell model to noninteger order derivatives. We present and discuss formulations of the fractional order viscoelastic model and give physical interpretations of the model by using viscoelastic functions.
Nikita Bhangale, Krunal B. Kachhia, J. F. Gómez‐Aguilar   +2 more
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NONCONSERVATIVE SYSTEMS WITHIN FRACTIONAL GENERALIZED DERIVATIVES

IFAC Proceedings Volumes, 2006
A fractional derivative generalizes an ordinary derivative, and therefore the derivative of the product of two functions differs from that for the classical (integer) case; the integration by parts for Riemann-Liouville fractional derivatives involves both the left and right fractional derivatives.
Baleanu, Dumitru, Muslih, Sami I.
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Finite Fractional Sturm–Liouville Transforms For Generalized Fractional Derivatives

Iranian Journal of Science and Technology, Transactions A: Science, 2017
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Eshaghi, Shiva, Ansari, Alireza
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Generalized fractional derivatives generated by a class of local proportional derivatives

The European Physical Journal Special Topics, 2017
Recently, Anderson and Ulness [Adv. Dyn. Syst. Appl. 10, 109 (2015)] utilized the concept of the proportional derivative controller to modify the conformable derivatives. In parallel to Anderson’s work, Caputo and Fabrizio [Progr. Fract. Differ. Appl.
Fahd Jarad, Thabet Abdeljawad, Jehad Alzabut   +2 more
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Mikusiński’s operational calculus for general conjugated fractional derivatives

Boletín de la Sociedad Matemática Mexicana, 2023
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Generalized fractional Schrödinger equation with space-time fractional derivatives

Journal of Mathematical Physics, 2007
In this paper the generalized fractional Schrödinger equation with space and time fractional derivatives is constructed. The equation is solved for free particle and for a square potential well by the method of integral transforms, Fourier transform and Laplace transform, and the solution can be expressed in terms of Mittag-Leffler function.
Wang, Shaowei, Xu, Mingyu
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Fractional Left Local General M-Derivative

2020
Here is introduced and studied the left fractional local general M-derivative of various orders. All basic properties of an ordinary derivative are established here. We also define the corresponding left fractional M-integrals. Important theorems are established such as: the inversion theorem, the fundamental theorem of fractional calculus, the mean ...
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