Results 21 to 30 of about 1,446 (157)

On a nonlocal implicit problem under Atangana–Baleanu–Caputo fractional derivative

Boundary Value Problems, 2021
In this paper, we study a class of initial value problems for a nonlinear implicit fractional differential equation with nonlocal conditions involving the Atangana–Baleanu–Caputo fractional derivative.
Abeer S. Alnahdi, Mdi Begum Jeelani, Mohammed S. Abdo, Saeed M. Ali, S. Saleh   +4 more
doaj   +1 more source

Stability of Nonlinear Implicit Differential Equations with Caputo–Katugampola Fractional Derivative

Mathematics, 2023
The purpose of this paper is to study nonlinear implicit differential equations with the Caputo–Katugampola fractional derivative. By using Gronwall inequality and Banach fixed-point theorem, the existence of the solution of the implicit equation is ...
Qun Dai, Yunying Zhang
doaj   +1 more source

Fractional Order Runge–Kutta Methods

Fractal and Fractional, 2023
This paper presents a new class of fractional order Runge–Kutta (FORK) methods for numerically approximating the solution of fractional differential equations (FDEs).
Farideh Ghoreishi, Rezvan Ghaffari, Nasser Saad   +2 more
doaj   +1 more source

Ulam-type stability for a class of implicit fractional differential equations with non-instantaneous integral impulses and boundary condition

Advances in Difference Equations, 2017
In this paper, we investigate four different types of Ulam stability, i.e., Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for a class of nonlinear implicit fractional ...
Akbar Zada, Sartaj Ali, Yongjin Li
doaj   +1 more source

Terminal Value Problem for Implicit Katugampola Fractional Differential Equations in b-Metric Spaces

Journal of Function Spaces, 2021
This manuscript deals with a class of Katugampola implicit fractional differential equations in b-metric spaces. The results are based on the α−φ-Geraghty type contraction and the fixed point theory. We express an illustrative example.
Salim Krim, Saïd Abbas, Mouffak Benchohra, Erdal Karapinar   +3 more
doaj   +1 more source

Impulsive boundary value problems for nonlinear implicit Caputo-exponential type fractional differential equations

Electronic Journal of Qualitative Theory of Differential Equations, 2020
This paper deals with existence and uniqueness of solutions to a class of impulsive boundary value problem for nonlinear implicit fractional differential equations involving the Caputo-exponential fractional derivative. The existence results are based on
Ahmed Malti, Mouffak Benchohra, John Graef, Jamal-Eddine Lazreg   +3 more
doaj   +1 more source

Neutral functional sequential differential equations with Caputo fractional derivative on time scales

Fixed Point Theory and Algorithms for Sciences and Engineering, 2022
In this paper, we establish the existence and uniqueness of a solution for a class of initial value problems for implicit fractional differential equations with Caputo fractional derivative.
Jamal Eddine Lazreg, Nadia Benkhettou, Mouffak Benchohra, Erdal Karapinar   +3 more
doaj   +1 more source

Implicit analytic solutions for a nonlinear fractional partial differential beam equation [PDF]

Communications in Nonlinear Science and Numerical Simulation, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Konstantinos Liaskos, Athanasios A. Pantelous, Ioannis A. Kougioumtzoglou, Antonios T. Meimaris, Antonina Pirrotta   +4 more
openaire   +2 more sources

Boundary Value Problem for Fractional Order Generalized Hilfer-Type Fractional Derivative with Non-Instantaneous Impulses

Fractal and Fractional, 2020
This manuscript is devoted to proving some results concerning the existence of solutions to a class of boundary value problems for nonlinear implicit fractional differential equations with non-instantaneous impulses and generalized Hilfer fractional ...
Abdelkrim Salim, Mouffak Benchohra, John R. Graef, Jamal Eddine Lazreg   +3 more
doaj   +1 more source

THEORY OF FRACTIONAL IMPLICIT DIFFERENTIAL EQUATIONS WITH COMPLEX ORDER

Journal of Universal Mathematics, 2019
In this paper, we consider boundary value problems for the following nonlinear implicit differential equations with complex order D +x(t) = f t,x(t),D +x(t) , ? = m+i?, t ? J := [0,T],  ax(0)+bx(T) = c,where D + is the Caputo fractional derivative of order ? ? C. Let ? ? R , 0 < ? < 1, m ? (0,1], and f : J ×R ?
Elsayed ELSAYED, D. VİVEK, K. KANAGARAJAN   +2 more
openaire   +3 more sources