Results 91 to 100 of about 1,565,786 (254)

Variable order Mittag-Leffler fractional operators on isolated time scales and application to the calculus of variations

, 2018
We introduce new fractional operators of variable order on isolated time scales with Mittag-Leffler kernels. This allows a general formulation of a class of fractional variational problems involving variable-order difference operators.
A Atangana, A Atangana, A Atangana, A Atangana, A Atangana, A Coronel-Escamilla, A Coronel-Escamilla, A Coronel-Escamilla, B Pei, B Ross, Benaoumeur Bayour, C Goodrich, CF Lorenzo, CFM Coimbra, CJ Zúñiga-Aguilar, D Tavares, D Tavares, D Tavares, D Tavares, G Diaz, J Losada, J Tang, JE Solís-Pérez, JF Gómez-Aguilar, JF Gómez-Aguilar, JF Gómez-Aguilar, JF Gómez-Aguilar, K Sheng, LES Ramirez, LES Ramirez, M Caputo, M Caputo, N Benkhettou, Nadia Benkhettou, NRO Bastos, NRO Bastos, NRO Bastos, R Almeida, RB Nelsen, SG Samko, SG Samko, SG Samko, T Abdeljawad, T Abdeljawad, T Abdeljawad, T Abdeljawad, TM Atanackovic, VF Morales-Delgado, Y Hang   +48 more
core   +1 more source

A highly accurate numerical method for solving boundary value problem of generalized Bagley‐Torvik equation

Mathematical Methods in the Applied Sciences, EarlyView.
A highly accurate numerical method is given for the solution of boundary value problem of generalized Bagley‐Torvik (BgT) equation with Caputo derivative of order 0<β<2$$ 0<\beta <2 $$ by using the collocation‐shooting method (C‐SM). The collocation solution is constructed in the space Sm+1(1)$$ {S}_{m+1}^{(1)} $$ as piecewise polynomials of degree at ...
Suzan Cival Buranay, Mtema James Chin, Nazim I. Mahmudov   +2 more
wiley   +1 more source

The fractional Dodson diffusion equation: a new approach

, 2018
In this paper, after a brief review of the general theory concerning regularized derivatives and integrals of a function with respect to another function, we provide a peculiar fractional generalization of the $(1+1)$-dimensional Dodson's diffusion ...
Garra, Roberto, Giusti, Andrea, Mainardi, Francesco   +2 more
core   +1 more source

Exponential Stability of Higher Order Fractional Neutral Stochastic Differential Equation Via Integral Contractors

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, Dhanalakshmi Kasinathan, Ramkumar Kasinathan, Ravikumar Kasinathan   +3 more
wiley   +1 more source

Multiterm boundary value problem of Caputo fractional differential equations of variable order

Advances in Difference Equations, 2021
In this manuscript, the existence, uniqueness, and stability of solutions to the multiterm boundary value problem of Caputo fractional differential equations of variable order are established.
Zoubida Bouazza, Mohammed Said Souid, Hatıra Günerhan   +2 more
doaj   +1 more source

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

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

Post-Pandemic Sector-Based Investment Model Using Generalized Liouville–Caputo Type

Symmetry, 2023
In this article, Euler’s technique was employed to solve the novel post-pandemic sector-based investment mathematical model. The solution was established within the framework of the new generalized Caputo-type fractional derivative for the system under consideration that serves as an example of the investment model.
Muath Awadalla, Muthaiah Subramanian, Prakash Madheshwaran, Kinda Abuasbeh   +3 more
openaire   +1 more source

A Numerical Method Combining Cubic Interpolated Propagation and Shifted Grünwald–Letnikov for Fractional Advection–Dispersion Equations

International Journal for Numerical and Analytical Methods in Geomechanics, EarlyView.
ABSTRACT Recent advances in the numerical solution of fractional partial differential equations have yielded promising results. In particular, the Shifted Grünwald–Letnikov (SGL) approach allows for a generalization of the traditional finite difference method to the context of fractional differential equations.
Pedro Victor Serra Mascarenhas, André Luís Brasil Cavalcante   +1 more
wiley   +1 more source

A Gronwall inequality for a general Caputo fractional operator [PDF]

Mathematical Inequalities & Applications, 2017
In this paper we present a new type of fractional operator, which is a generalization of the Caputo and Caputo--Hadamard fractional derivative operators. We study some properties of the operator, namely we prove that it is the inverse operation of a generalized fractional integral.
openaire   +3 more sources