Results 21 to 30 of about 15,213 (267)
Mathematics, 2021 In this paper, we study the recently proposed fractional-order operators with general analytic kernels. The kernel of these operators is a locally uniformly convergent power series that can be chosen adequately to obtain a family of fractional operators ...
Oscar Martínez-Fuentes +3 more
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Fractional derivatives in spaces of generalized functions [PDF]
Fractional Calculus and Applied Analysis, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the Basic Theory of Some Generalized and Fractional Derivatives
Fractal and Fractional, 2022 We continue the development of the basic theory of generalized derivatives as introduced and give some of their applications. In particular, we formulate necessary conditions for extrema, Rolle’s theorem, the mean value theorem, the fundamental theorem of calculus, integration by parts, along with an existence and uniqueness theorem for a generalized ...
Leila Gholizadeh Zivlaei +1 more
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Results in Physics, 2022 The current research is about new exact soliton solutions to the Cahn–Allen equation and Predator–Prey model with the most general fractional derivative operator.
Shao-Wen Yao +5 more
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Fractional derivative generalization of Noether’s theorem
Open Mathematics, 2015 Abstract The symmetry of the Bagley–Torvik equation is investigated by using the Lie group analysis method. The Bagley–Torvik equation in the sense of the Riemann–Liouville derivatives is considered. Then we prove a Noetherlike theorem for fractional Lagrangian densities with the Riemann-Liouville fractional derivative and few examples ...
Khorshidi Maryam +2 more
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Generalized solutions of the fractional Burger’s equation
Results in Physics, 2019 We investigate the solutions for the fractional Burger’s equation based on the Jumarie fractional derivative using Bernoulli polynomials. We find general solutions for such problems. Comparison with other methods is presented.
Muhammed I. Syam +4 more
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Fractal and Fractional, 2023 In this paper, we investigate the necessary conditions to optimize a given functional, involving a generalization of the tempered fractional derivative.
Ricardo Almeida
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New theoretical results and applications on conformable fractional Natural transform
Ain Shams Engineering Journal, 2021 In this paper, we proceed on to develop the classical Natural transform to fractional order in the sense of conformable derivative and set the basic concepts in this new interesting fractional transform version.
Zeyad Al-Zhour +3 more
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Generalized Taylor’s formula for power fractional derivatives
Boletín de la Sociedad Matemática Mexicana, 2023 AbstractWe establish a new generalized Taylor’s formula for power fractional derivatives with nonsingular and nonlocal kernels, which includes many known Taylor’s formulas in the literature. Moreover, as a consequence, we obtain a general version of the classical mean value theorem.
Hanaa Zitane, Delfim F. M. Torres
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A maximum principle for a fractional boundary value problem with convection term and applications
Mathematical Modelling and Analysis, 2019 We consider a fractional boundary value problem with Caputo-Fabrizio fractional derivative of order 1 < α < 2 We prove a maximum principle for a general linear fractional boundary value problem.
Mohammed Al-Refai, Kamal Pal
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