Results 11 to 20 of about 1,241 (197)

Hyers-Ulam-Rassias Stability of some sequential neutral functional differential equations with Caputo-Hadamard fractional derivative

Miskolc Mathematical Notes
In this article, we employ a fixed point theory to investigate the stability in the sense of Hyers-Ulam-Rassias of some sequential neutral functional differential equations with Caputo-Hadamard fractional derivative. We present two examples to illustrate
Abdellatif Ben Makhlouf, El-sayed El-hady   +1 more
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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
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Numerical solution of coupled fractional Ginzburg–Landau equations under Caputo–Hadamard derivative

Results in Physics
This 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, M.H. Heydari, M. Bayram, D. Baleanu   +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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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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Compact and Noncompact Solutions to Generalized Sturm–Liouville and Langevin Equation with Caputo–Hadamard Fractional Derivative [PDF]

Mathematical Problems in Engineering, 2021
In this work, through using the Caputo–Hadamard fractional derivative operator with three nonlocal Hadamard fractional integral boundary conditions, a new type of the fractional-order Sturm–Liouville and Langevin problem is introduced. The existence of solutions for this nonlinear boundary value problem is theoretically investigated based on the ...
Ahmed Salem, Noorah Mshary, Moustafa El-Shahed, Faris Alzahrani   +3 more
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Lyapunov-type inequalities for fractional Langevin-type equations involving Caputo-Hadamard fractional derivative

Journal of Inequalities and Applications, 2022
AbstractIn this study, some new Lyapunov-type inequalities are presented for Caputo-Hadamard fractional Langevin-type equations of the forms $$ \begin{aligned} &{}_{H}^{C}D_{a + }^{\beta } \bigl({}_{H}^{C}D_{a + }^{\alpha }+ p(t)\bigr)x(t) + q(t)x(t) = 0,\quad 0 < a < t < b, \end{aligned} $$
Wei Zhang, Jifeng Zhang, Jinbo Ni
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An Initial Value Problem Involving Caputo-Hadamard Fractional Derivative: The Extremal Solutions and Stabilization

Journal of Advanced Engineering and Computation, 2020
In this paper, the existence of extremal solutions of Caputo-Hadamard-type fractional differential equations (CHFDEs) with order $\alpha \in (1,2)$ is established by employing the method of lower and upper solutions. Moreover, sufficient condition that ensures the stability of a class of CHFDE is also provided. Some examples are given to illustrate our
Donal O'Regan, Ngo Van Hoa
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Existence of Solutions for a Coupled System of p-Laplacian Caputo–Hadamard Fractional Sturm–Liouville–Langevin Equations with Antiperiodic Boundary Conditions

Journal of Mathematics, 2022
Fractional Sturm–Liouville and Langevin equations have recently attracted much attention. In this paper, we investigate a coupled system of fractional Sturm–Liouville–Langevin equations with antiperiodic boundary conditions in the framework of Caputo ...
Jinbo Ni, Jifeng Zhang, Wei Zhang
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Solving Coupled Impulsive Fractional Differential Equations With Caputo-Hadamard Derivatives in Phase Spaces

International Journal of Analysis and Applications, 2023
In this manuscript, we incorporate Caputo-Hadamard derivatives in impulsive fractional differential equations to obtain a new class of impulsive fractional form. Further, the existence of solutions to the proposed problem has been inferred under a state-dependent delay and suitable hypotheses in phase spaces.
Hasanen A. Hammad, Hassen Aydi, Doha A. Kattan   +2 more
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