Results 81 to 90 of about 38,304 (201)

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  

Implicit cubic B-spline scheme for the fractional Black-Scholes model with Caputo-Hadamard derivative [PDF]

Journal of Mahani Mathematical Research
In this study, we introduce a novel numerical scheme for solving the Black–Scholes equation endowed with a Caputo-Hadamard fractional time derivative. The temporal derivative is discretized via a finite-difference approach, ensuring both stability and ...
Roya Montazeri
doaj   +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  

An analogue of Leibniz’s rule for Hadamard derivatives and their application

Қарағанды университетінің хабаршысы. Математика сериясы
This paper explores new analogues of the Leibniz rule for Hadamard and Caputo–Hadamard fractional derivatives. Unlike classical derivatives, fractional ones have a strong nonlocal character, meaning that the value of the derivative at a given point ...
A.G. Smadiyeva
doaj   +1 more source