Results 1 to 10 of about 582,712 (204)

Caputo Fractional Derivative Hadamard Inequalities for Strongly m-Convex Functions

Journal of Function Spaces, 2021
In this paper, two versions of the Hadamard inequality are obtained by using Caputo fractional derivatives and strongly m-convex functions. The established results will provide refinements of well-known Caputo fractional derivative Hadamard inequalities ...
Xue Feng, Baolin Feng, Ghulam Farid, Sidra Bibi, Qi Xiaoyan, Ze Wu   +5 more
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A Survey on Recent Results on Lyapunov-Type Inequalities for Fractional Differential Equations

Fractal and Fractional, 2022
This survey paper is concerned with some of the most recent results on Lyapunov-type inequalities for fractional boundary value problems involving a variety of fractional derivative operators and boundary conditions.
Sotiris K. Ntouyas, Bashir Ahmad, Jessada Tariboon   +2 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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A comprehensive review of the Hermite-Hadamard inequality pertaining to fractional differential operators [PDF]

Surveys in Mathematics and its Applications, 2023
A review on Hermite-Hadamard type inequalities connected with a different classes of convexities and fractional differential operators is presented. In the various classes of convexities it includes, classical convex functions, quasi-convex functions, p ...
Muhammad Tariq, Sotiris K. Ntouyas, Asif Ali Shaikh, Jessada Tariboon   +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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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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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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Impulsive fractional differential equations with state-dependent delay involving the Caputo-Hadamard derivative

Filomat, 2023
In this paper, we investigate the existence of solutions for a class of initial value problems for impulsive Caputo-Hadamard fractional differential equations with state-dependent delay.
Amouria Hammou, Samira Hamani, Johnny Henderson   +2 more
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