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
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Implicit cubic B-spline scheme for the fractional Black-Scholes model with Caputo-Hadamard derivative [PDF]
Journal of Mahani Mathematical ResearchIn 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
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Boundary Value ProblemsIn this manuscript, we investigated the existence, uniqueness, and Ulam–Hyers stability results of solutions to implicit Caputo–Hadamard fractional differential equations with noninstantaneous impulses and δ − d e r i v a t i v e $\delta -derivative ...
Mesfin Teshome Beyene +2 more
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Numerical solution of coupled fractional Ginzburg–Landau equations under Caputo–Hadamard derivative
Results in PhysicsThis paper introduces a high-performance spectral collocation method for solving coupled fractional Ginzburg–Landau equations involving the Caputo–Hadamard (CH) derivative. The numerical scheme employees two families of shifted Chebyshev polynomials (CPs)
F. Rostami +3 more
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Convergence analysis of positive solution for Caputo–Hadamard fractional differential equation [PDF]
Nonlinear AnalysisBy deriving the expression of Green function and some of its special properties and establishing appropriate substitution and appropriate cone, the existence of unique iterative positive, error estimation, and convergence rate of approximate solution ...
Limin Guo +3 more
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Caputo–Hadamard Fractional Derivatives of Variable Order [PDF]
Numerical Functional Analysis and Optimization, 2016 ABSTRACTIn this article, we present three types of Caputo–Hadamard derivatives of variable fractional order and study the relations between them. An approximation formula for each fractional operator, using integer-order derivatives only, is obtained and an estimation for the error is given.
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Qualitative Analysis of Stochastic Caputo–Katugampola Fractional Differential Equations [PDF]
AxiomsStochastic pantograph fractional differential equations (SPFDEs) combine three intricate components: stochastic processes, fractional calculus, and pantograph terms.
Zareen A. Khan +3 more
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Integral Boundary Value Problems for Implicit Fractional Differential Equations Involving Hadamard and Caputo-Hadamard fractional Derivatives [PDF]
Kragujevac Journal of Mathematics, 2021 In this paper, we examine the existence and uniqueness of integral boundary value problem for implicit fractional differential equations (IFDE’s) involving Hadamard and Caputo-Hadamard fractional derivative. We prove the existence and uniqueness results by utilizing Banach and Schauder’s fixed point theorem.
Karthikeyan, P., Arul, R.
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Boundary value problems for Caputo-Hadamard fractional differential inclusions in Banach spaces [PDF]
, 2022 summary:In this article, we study the existence of solutions in a Banach space of boundary value problems for Caputo-Hadamard fractional differential inclusions of order $r \in (0,1]$
Hammou, Amouria +2 more
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BOUNDARY VALUE PROBLEM FOR NONLINEAR CAPUTO-HADAMARD FRACTIONAL DIFFERENTIAL EQUATION WITH HADAMARD FRACTIONAL INTEGRAL AND ANTI-PERIODIC CONDITIONS [PDF]
, 2021 The aim of this work is to study a class of boundary value problem including a fractional order differential equation involving the Caputo-Hadamard fractional derivative. Suffcient conditions will be presented to guarantee the existence and uniqueness of
Boutiara, Abdelatif +2 more
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