Results 21 to 30 of about 3,215 (223)
Journal of Function Spaces, 2020 In this article, radial basis function collocation scheme is adopted for the numerical solution of fractional partial differential equations. This method is highly demanding because of its meshless nature and ease of implementation in high dimensions and
Mehnaz Shakeel +5 more
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Incomplete Caputo fractional derivative operators
Advances in Difference Equations, 2018 The main aim of this paper is to give the definitions of Caputo fractional derivative operators and show their use in the special function theory. For this purpose, we introduce new types of incomplete hypergeometric functions and obtain their integral ...
Mehmet Ali Özarslan, Ceren Ustaoglu
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A novel equivalent definition of Caputo fractional derivative without singular kernel and superconvergent analysis [PDF]
Journal of Mathematical Physics, 2018 In this article, we present a new second-order finite difference discrete scheme for a fractal mobile/immobile transport model based on equivalent transformative Caputo formulation. The new transformative formulation takes the singular kernel away to make the integral calculation more efficient. Furthermore, this definition is also effective where α is
Liu, Zhengguang, Li, Xiaoli
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Fractional Cauchy Problem with Caputo Nabla Derivative on Time Scales
Abstract and Applied Analysis, 2015 The definition of Caputo fractional derivative is given and some of its properties are discussed in detail. After then, the existence of the solution and the dependency of the solution upon the initial value for Cauchy type problem with fractional Caputo
Jiang Zhu, Ling Wu
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Scientific Reports, 2022 In this paper, we have been study a hybrid nanofluid over an exponentially oscillating vertical flat plate. Therefore the fractional derivatives definition of Caputo–Fabrizio approach is applied to transform the classical model for this hybrid nanofluid ...
Sami Ul Haq +5 more
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Alexandria Engineering Journal, 2020 The present paper consider a newly introduced operator known as fractal-fractional where the fractional operator considered is Caputo-Fabrizio. We consider a competition system and propose the field data of banks for 2004–2014 of Indonesia banks of the ...
Abdon Atangana +2 more
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Fractional Probability Theory of Arbitrary Order
Fractal and Fractional, 2023 A generalization of probability theory is proposed by using the Riemann–Liouville fractional integrals and the Caputo and Riemann–Liouville fractional derivatives of arbitrary (non-integer and integer) orders. The definition of the fractional probability
Vasily E. Tarasov
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International Journal of Numerical Methods and Applications, 2018 Summary: In this paper, linear fractional Schrödinger equation is studied by using compact finite differences method. The fractional part of the equation is worked by applying Caputo fractional derivative definition. In the solution of the problem, finite differences discretization along the time, and fifth-order compact finite differences scheme along
Er, Neslihan +2 more
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A hybrid B-spline collocation technique for the Caputo time fractional nonlinear Burgers’ equation
Beni-Suef University Journal of Basic and Applied Sciences, 2023 Background This study proposes an efficient and stable technique based on new hybrid B-spline (HB-spline) functions for the numerical treatment of the Caputo time fractional nonlinear Burgers’ (TFNB) equation. The time derivative is discretized using the
Mohammad Tamsir +3 more
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Scientific Reports, 2021 In this paper, we investigate an norovirus (NoV) epidemic model with stochastic perturbation and the new definition of a nonlocal fractal–fractional derivative in the Atangana–Baleanu–Caputo (ABC) sense.
Ting Cui, Peijiang Liu, Anwarud Din
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