Results 71 to 80 of about 21,294 (235)
Caputo-Type Modification of the Erdélyi-Kober Fractional Derivative [PDF]
, 2007 2000 Math. Subject Classification: 26A33; 33E12, 33E30, 44A15, 45J05The Caputo fractional derivative is one of the most used definitions of a fractional derivative along with the Riemann-Liouville and the Grünwald- Letnikov ones.
Luchko, Yury, Trujillo, Juan
core
Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6425-6446, April 2025.ABSTRACT The well‐posedness results for mild solutions to the fractional neutral stochastic differential system with Rosenblatt process with Hurst index Ĥ∈12,1$$ \hat{H}\in \left(\frac{1}{2},1\right) $$ is discussed in this article. To demonstrate the results, the concept of bounded integral contractors is combined with the stochastic result and ...
Dimplekumar N. Chalishajar +3 more
wiley +1 more source
Advances in Mathematical PhysicsThis paper presents an efficient numerical scheme for the space–time tempered fractional convection–diffusion equation, where the time derivative is the Caputo-tempered fractional derivative and the space derivatives are the normalized left and right ...
Dechao Gao +3 more
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On the Solutions Fractional Riccati Differential Equation with Modified Riemann-Liouville Derivative
International Journal of Differential Equations, 2012 Fractional variational iteration method (FVIM) is performed to give an approximate analytical solution of nonlinear fractional Riccati differential equation. Fractional derivatives are described in the Riemann-Liouville derivative.
Mehmet Merdan
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A New Generalized Definition of Fractional Derivative with Non-Singular Kernel
Computation, 2020 This paper proposes a new definition of fractional derivative with non-singular kernel in the sense of Caputo which generalizes various forms existing in the literature. Furthermore, the version in the sense of Riemann–Liouville is defined.
Khalid Hattaf
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Filomat, 2019 The purpose of this paper is to study the existence and multiplicity of solutions to the following Kirchhoff equation with singular nonlinearity and Riemann-Liouville Fractional Derivative: (P?){a+b ?T0|0D?t(u(t))|pdt)p-1 tD?T (?p(0D?tu(t)) = ?g(t)/u ...
M. Kratou
semanticscholar +1 more source
Fractional Cauchy Problem with Riemann-Liouville Derivative on Time Scales [PDF]
Abstract and Applied Analysis, 2013 Summary: \(\nabla\)-Laplace transform, fractional \(\nabla\)-power function, \(\nabla\)-Mittag-Leffler function, fractional \(\nabla\)-integrals, and fractional \(\nabla\)-differential on time scales are defined. Some of their properties are discussed in detail.
Ling Wu, Jiang Zhu
openaire +3 more sources
Equivalences of Nonlinear Higher Order Fractional Differential Equations With Integral Equations
Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6930-6942, April 2025.ABSTRACT Equivalences of initial value problems (IVPs) of both nonlinear higher order (Riemann–Liouville type) fractional differential equations (FDEs) and Caputo FDEs with the corresponding integral equations are studied in this paper. It is proved that the nonlinearities in the FDEs can be L1$$ {L}^1 $$‐Carathéodory with suitable conditions.
Kunquan Lan
wiley +1 more source
On Impulsive Boundary Value Problem with Riemann-Liouville Fractional Order Derivative
Journal of Function Spaces, 2021 Our manuscript is devoted to investigating a class of impulsive boundary value problems under the concept of the Riemann-Liouville fractional order derivative. The subject problem is of implicit type. We develop some adequate conditions for the existence
Zareen A. Khan, Rozi Gul, Kamal Shah
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, 2016 We present a new way of constructing a fractional-based convolution mask with an application to image edge analysis. The mask was constructed based on the Riemann-Liouville fractional derivative which is a special form of the Srivastava-Owa operator ...
Peter Amoako-Yirenkyi +2 more
semanticscholar +1 more source