Results 11 to 20 of about 35,805 (203)

Stability analysis for a class of implicit fractional differential equations involving Atangana-Baleanu fractional derivative. [PDF]

Adv Differ Equ, 2021
AbstractSome fundamental conditions and hypotheses are established to ensure the existence, uniqueness, and stability to a class of implicit boundary value problems (BVPs) with Atangana–Baleanu–Caputo type derivative and integral. The required results are established by utilizing the Banach contraction mapping principle and fixed point theorem of ...
Asma, Shabbir S, Shah K, Abdeljawad T.
europepmc   +7 more sources

Implicit nonlinear fractional differential equations of variable order [PDF]

Boundary Value Problems, 2021
In this manuscript, we examine both the existence and the stability of solutions to the implicit boundary value problem of Caputo fractional differential equations of variable order.
Amar Benkerrouche, Mohammed Said Souid, Kanokwan Sitthithakerngkiet, Ali Hakem   +3 more
doaj   +3 more sources

Implicit Fractional Differential Equations via the Liouville–Caputo Derivative [PDF]

Mathematics, 2015
We study an initial value problem for an implicit fractional differential equation with the Liouville–Caputo fractional derivative. By using fixed point theory and an approximation method, we obtain some existence and uniqueness results.
Juan J. Nieto, Abelghani Ouahab, Venktesh Venktesh   +2 more
doaj   +3 more sources

On stability for nonlinear implicit fractional differential equations

Le Matematiche, 2015
The purpose of this paper is to establish some  types of Ulam stability: Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for a class of implicit fractional-order ...
Mouffak Benchohra, Jamal E. Lazreg
doaj   +2 more sources

Nonlocal boundary value problem for generalized Hilfer implicit fractional differential equations [PDF]

Mathematical Methods in the Applied Sciences, 2020
In this paper, we derive the equivalent fractional integral equation to the nonlinear implicit fractional differential equations involving Ψ‐Hilfer fractional derivative subject to nonlocal fractional integral boundary conditions. The existence of a solution, Ulam–Hyers, and Ulam–Hyers–Rassias stability have been acquired by means of an equivalent ...
Ashwini D. Mali, Kishor D. Kucche
openaire   +4 more sources

Qualitative Study on Solutions of Piecewise Nonlocal Implicit Fractional Differential Equations

Journal of Function Spaces, 2023
In this paper, we investigate new types of nonlocal implicit problems involving piecewise Caputo fractional operators. The existence and uniqueness results are proved by using some fixed point theorems. Furthermore, we present analogous results involving piecewise Caputo-Fabrizio and Atangana–Baleanu fractional operators.
Mohammed S. Abdo, Sahar Ahmed Idris, Wedad Albalawi, Abdel‐Haleem Abdel‐Aty, Mohammed Zakarya, Emad E. Mahmoud   +5 more
openaire   +4 more sources

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   +2 more sources

Efficient Hybrid ANN-Accelerated Two-Stage Implicit Schemes for Fractional Differential Equations

Mathematics
This paper introduces a hybrid two-stage implicit scheme for efficiently solving fractional differential equations, with particular emphasis on fractional initial value problems formulated using the Caputo derivative.
Mudassir Shams, Bruno Carpentieri
doaj   +2 more sources

Existence results for nonlinear implicit fractional differential equations [PDF]

Surveys in Mathematics and its Applications, 2014
In this paper, we establish the existence and uniqueness of solution for a class of initial value problem for implicit fractional differential equations with Caputo fractional derivative.
Mouffak Benchohra , Jamal Eddine Lazreg
doaj   +2 more sources

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   +2 more sources