Results 91 to 100 of about 1,241 (197)
International Journal of Differential Equations, Volume 2025, Issue 1, 2025.In order to solve fractional differential equations on quantum domains, this work provides a spectral approach based on higher‐order (q, τ)‐Bernoulli functions and polynomials. We build a robust basis for approximation in (q, τ)‐weighted Hilbert spaces by using the orthogonality properties of these extended polynomials and the Sheffer‐type generating ...
Shaher Momani +2 more
wiley +1 more source
Results in Applied MathematicsIn this study, we develop an operational matrix technique to address a set of fractional nonlinear integro-differential equations with the Caputo–Hadamard derivative. We utilize a family of the piecewise Chebyshev cardinal functions as basis functions in
S. Mansoori Aref +2 more
doaj +1 more source
Solvability of Implicit Fractional Systems With Nonlocal Conditions in Weighted Functional Spaces
International Journal of Differential Equations, Volume 2025, Issue 1, 2025.This paper investigates the existence and uniqueness of solutions for a class of nonlinear implicit Riemann–Liouville fractional integro‐differential equations subject to nonlocal conditions in a weighted Banach space. The inclusion of both implicit effects and nonlocal terms introduces additional complexity, making the analysis both challenging and ...
Abdulrahman A. Sharif +3 more
wiley +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 +1 more
core
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
Results in PhysicsThis paper employs the Caputo–Hadamard derivative to create the coupled nonlinear fractional Ginzburg–Landau equations. An orthonormal version of the discrete Legendre polynomials is utilized to generate a numerical strategy for this system.
M.H. Heydari, D. Baleanu, M. Bayram
doaj +1 more source
A Discretization of the Hadamard fractional derivative [PDF]
, 2016 We present a new discretization for the Hadamard fractional derivative, that simplifies the computations. We then apply the method to solve a fractional differential equation and a fractional variational problem with dependence on the Hadamard ...
Almeida, Ricardo, Bastos, Nuno
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A Boundary Value Problem with Caputo–Hadamard Fractional Derivative: Analysis and Numerical Solution
European Journal of Pure and Applied MathematicsWe investigate a boundary-value problem governed by a fractional differential equation, which is non-linear. The fractional derivative is the combined Caputo-Hadamard fractional derivative. We establish the required conditions for the existence and uniqueness of solutions utilising the two standard fixed-point theorems, Banach fixed-point and Sadovskii
Afrah Hasan, Shayma Murad
openaire +1 more source
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. +2 more
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On Some Impulsive Fractional Integro-Differential Equation with Anti-Periodic Conditions
Fractal and FractionalWe investigate a class of boundary value problems (BVPs) involving an impulsive fractional integro-differential equation (IF-IDE) with the Caputo–Hadamard fractional derivative (C-HFD). We employ some fixed-point theorems (FPTs) to study the existence of
Ymnah Alruwaily +2 more
doaj +1 more source