Results 51 to 60 of about 12,535 (181)

Wirtinger-type inequalities for Caputo fractional derivatives via Taylor’s formula

Journal of Inequalities and Applications
In this study, we firstly derive a Wirtinger-type result, which gives the connection in between the integral of square of a function and the integral of square of its Caputo fractional derivatives with the help of left-sided and right-sided fractional ...
Samet Erden, Mehmet Zeki Sarıkaya, Burçin Gokkurt Ozdemir, Neslihan Uyanık   +3 more
doaj   +1 more source

Caputo Fractional Derivative Hadamard Inequalities for Strongly m-Convex Functions

Journal of Function Spaces, 2021
In this paper, two versions of the Hadamard inequality are obtained by using Caputo fractional derivatives and strongly m-convex functions. The established results will provide refinements of well-known Caputo fractional derivative Hadamard inequalities ...
Xue Feng, Baolin Feng, Ghulam Farid, Sidra Bibi, Qi Xiaoyan, Ze Wu   +5 more
doaj   +1 more source

GENERALIZED LAPLACE TRANSFORM AND TEMPERED Ψ-CAPUTO FRACTIONAL DERIVATIVE

Mathematical Modelling and Analysis, 2023
In this paper, images of the tempered Ψ-Hilfer fractional integral and the tempered Ψ-Caputo fractional derivative under the generalized Laplace transform are derived. The results are applied to find a solution to an initial value problem for a nonhomogeneous linear fractional differential equation with the tempered Ψ-Caputo fractional derivative of an
Milan Medveď, Michal Pospíšil
openaire   +4 more sources

Non-existence of periodic solutions in fractional-order dynamical systems and a remarkable difference between integer and fractional-order derivatives of periodic functions

, 2011
Using the Mellin transform approach, it is shown that, in contrast with integer-order derivatives, the fractional-order derivative of a periodic function cannot be a function with the same period.
Kaslik, Eva, Sivasundaram, Seenith
core   +1 more source

Numerical Solutions of Certain New Models of the Time-Fractional Gray-Scott

Journal of Function Spaces, 2021
A reaction-diffusion system can be represented by the Gray-Scott model. In this study, we discuss a one-dimensional time-fractional Gray-Scott model with Liouville-Caputo, Caputo-Fabrizio-Caputo, and Atangana-Baleanu-Caputo fractional derivatives.
Sami Aljhani, Mohd Salmi Md Noorani, Khaled M. Saad, A. K. Alomari   +3 more
doaj   +1 more source

Pharmacokinetic/Pharmacodynamic anesthesia model incorporating psi-Caputo fractional derivatives

Computers in Biology and Medicine, 2023
We present a novel Pharmacokinetic/Pharmacodynamic (PK/PD) model for the induction phase of anesthesia, incorporating the $\psi$-Caputo fractional derivative. By employing the Picard iterative process, we derive a solution for a nonhomogeneous $\psi$-Caputo fractional system to characterize the dynamical behavior of the drugs distribution within a ...
Mohamed Abdelaziz Zaitri, Hanaa Zitane, Delfim F. M. Torres   +2 more
openaire   +4 more sources

The Variable-Order Fractional Calculus of Variations

, 2018
This book intends to deepen the study of the fractional calculus, giving special emphasis to variable-order operators. It is organized in two parts, as follows. In the first part, we review the basic concepts of fractional calculus (Chapter 1) and of the
Almeida, Ricardo, Tavares, Dina, Torres, Delfim F. M.   +2 more
core   +1 more source

On fractional derivatives with generalized Mittag-Leffler kernels

Advances in Difference Equations, 2018
Fractional derivatives with three parameter generalized Mittag-Leffler kernels and their properties are studied. The corresponding integral operators are obtained with the help of Laplace transforms.
Thabet Abdeljawad, Dumitru Baleanu
doaj   +1 more source

On the General Solutions of Some Non-Homogeneous Div-Curl Systems with Riemann–Liouville and Caputo Fractional Derivatives

Fractal and Fractional, 2021
In this work, we investigate analytically the solutions of a nonlinear div-curl system with fractional derivatives of the Riemann–Liouville or Caputo types.
Briceyda B. Delgado, Jorge E. Macías-Díaz   +1 more
doaj   +1 more source

Fractional advection differential equation within Caputo and Caputo–Fabrizio derivatives [PDF]

Advances in Mechanical Engineering, 2016
In this research, we applied the variational homotopic perturbation method and q-homotopic analysis method to find a solution of the advection partial differential equation featuring time-fractional Caputo derivative and time-fractional Caputo–Fabrizio derivative. A detailed comparison of the obtained results was reported.
Dumitru Băleanu, Bahram Agheli, Maysaa Mohamed Al Qurashi   +2 more
openaire   +2 more sources