Results 91 to 100 of about 13,452 (220)

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

Perturbed functional fractional differential equation of Caputo-Hadamard order [PDF]

Mathematica Moravica
In this paper, we investigate the existence of solution and extremal solutions for an initial-value problem of perturbed functional fractional differential equations with Caputo-Hadamard derivative.
Hamani Samira
doaj   +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

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

Weighted Weakly Singular Integral Inequalities: New Explicit Bounds and Applications in Fractional Dfferential Equations

Journal of Mathematics, Volume 2025, Issue 1, 2025.
This study delves into the formulation of innovative integral inequalities, specifically designed to accommodate weakly singular singularities, thus significantly broadening the scope of previously established ones. The methodology employed centers around the application of weighted fractional differential equations, leading to the derivation of a ...
Salah Boulares, Djalal Boucenna, Mohamed Rhaima, Lassaad Mchiri, Abdellatif Ben Makhlouf, Çetin Yildiz   +5 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  

Upper and lower solutions method for Caputo-Hadamard fractional differential inclusions [PDF]

Mathematica Moravica, 2019
In this paper, we use some background concerning multivalued functions and set-valued analysis, the fixed point theorem of Bohnenblust-Karlin and the method of upper and lower solutions to investigate the existence of solutions for a class of boundary ...
Abbas Saïd, Benchohra Mouffak, Hamani Samira, Henderson Johnny   +3 more
doaj  

A numerical approximation for the Caputo-Hadamard derivative and its application in time-fractional variable-coefficient diffusion equation

Discrete and Continuous Dynamical Systems - S
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhen Wang, Lu Sun
semanticscholar   +2 more sources

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