Results 41 to 50 of about 1,341,149 (142)

Advanced Fixed Point Methods for Analyzing Coupled Caputo Q‐Fractional Boundary Value Problems With Supportive Examples

Journal of Function Spaces, Volume 2025, Issue 1, 2025.
This article analyzes a complex coupled system of multipoint nonlinear boundary value problems involving Caputo‐type fractional discrete differential equations with multiple fractional q−integrals. We establish the uniqueness and existence of solutions using a rigorous approach grounded in fixed‐point theory, specifically Banach’s fixed‐point theorem ...
Hasanen A. Hammad, Saleh Fahad Aljurbua, Asamh Saleh M. Al Luhayb, Baowei Feng   +3 more
wiley   +1 more source

A new truncated $M$-fractional derivative type unifying some fractional derivative types with classical properties [PDF]

, 2017
We introduce a truncated $M$-fractional derivative type for $\alpha$-differentiable functions that generalizes four other fractional derivatives types recently introduced by Khalil et al., Katugampola and Sousa et al., the so-called conformable ...
de Oliveira, E. Capelas, Sousa, J. Vanterler da C.   +1 more
core   +3 more sources

Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives

, 2010
We prove optimality conditions for different variational functionals containing left and right Caputo fractional derivatives. A sufficient condition of minimization under an appropriate convexity assumption is given.
Agrawal, Agrawal, Agrawal, Agrawal, Agrawal, Agrawal, Almeida, Almeida, Atanacković, Blutzer, Delfim F.M. Torres, Dreisigmeyer, Dreisigmeyer, Frederico, Frederico, Inizan, Jónsson, Kilbas, Klimek, Klimek, Lorenzo, Mainardi, Malinowska Agnieszka, Miller, Muslih, Muslih, Podlubny, Ricardo Almeida, Riewe, Riewe, Samko, van Brunt   +31 more
core   +1 more source

Existence and Stability of Ulam–Hyers and Generalized Ulam–Hyers for the Generalized Langevin–Sturm–Liouville Equation Involving Generalized Liouville–Caputo Type

Journal of Mathematics, Volume 2025, Issue 1, 2025.
This paper focuses on investigating the existence, uniqueness, and stability of Ulam–Hyers (U‐H) and generalized Ulam–Hyers (G‐U‐H) solutions for the generalized Langevin–Sturm–Liouville equation, which involves generalized Liouville–Caputo derivatives and antiperiodic boundary conditions. We can divide this manuscript into six parts. The first section
Muthaiah Subramanian, Bundit Unyong, Muath Awadalla, Watcharaporn Cholamjiak   +3 more
wiley   +1 more source

On Improved Simpson‐Type Inequalities via Convexity and Generalized Fractional Operators

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this work, we develop novel Simpson‐type inequalities for mappings with convex properties by employing operators for tempered fractional integrals. These findings expand upon and refine classical results, including those linked to Riemann–Liouville fractional integrals.
Areej A. Almoneef, Abd-Allah Hyder, Fatih Hezenci, Hüseyin Budak, Pramita Mishra   +4 more
wiley   +1 more source

Numerical Methods for Solving Fractional Differential Equations [PDF]

, 2018
Department of Mathematical SciencesIn this thesis, several efficient numerical methods are proposed to solve initial value problems and boundary value problems of fractional di???erential equations.
Kim, Keon Ho
core  

Functional impulsive fractional differential inclusions involving the Caputo-Hadamard derivative

Mathematica Moravica
This paper establishes sufficient conditions for the existence of solutions to fractional impulsive functional differential inclusions, utilizing fixed-point theorems for multivalued mappings.
Aida Irguedi, S. Hamani
semanticscholar   +1 more source

The Generalized Fractional Calculus of Variations

, 2014
We review the recent generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives and study them using indirect methods.
Odzijewicz, Tatiana, Torres, Delfim F. M.   +1 more
core  

A Generalized Fractional Calculus of Variations

, 2013
We study incommensurate fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives and generalized fractional integrals and derivatives.
Malinowska, Agnieszka B., Odzijewicz, Tatiana, Torres, Delfim F. M.   +2 more
core  

Existence results for a fraction hybrid differential inclusion with Caputo–Hadamard type fractional derivative

Advances in Differential Equations, 2019
In this manuscript, we talk over the existence of solutions of a class of hybrid Caputo–Hadamard fractional differential inclusions with Dirichlet boundary conditions. Our results are based on the Arzelá–Ascoli theorem and some suitable theorems of fixed
M. Samei, V. Hedayati, S. Rezapour
semanticscholar   +1 more source