Results 31 to 40 of about 615,568 (200)
Fractional variational problems with the Riesz-Caputo derivative [PDF]
, 2012 In this paper we investigate optimality conditions for fractional variational problems, with a Lagrangian depending on the Riesz-Caputo derivative. First we prove a generalized Euler-Lagrange equation for the case when the interval of integration of the ...
Almeida, R., Ricardo Almeida
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Fractional variational problems depending on indefinite integrals [PDF]
, 2012 We obtain necessary optimality conditions for variational problems with a Lagrangian depending on a Caputo fractional derivative, a fractional and an indefinite integral.
Pooseh, Shakoor +8 more
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Numerical Methods for Caputo–Hadamard Fractional Differential Equations with Graded and Non-Uniform Meshes [PDF]
, 2021 We consider the predictor-corrector numerical methods for solving Caputo–Hadamard fractional differential equations with the graded meshes logtj=loga+logtNajNr,j=0,1,2,…,N with a≥1 and r≥1, where loga=logt0logt1⋯logtN=logT is a partition of [logt0,logT].
Yubin Yan +5 more
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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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On a Caputo-type fractional derivative
, 2019 In this paper, we present a new differential operator of arbitrary order defined by means of a Caputo-type modification of the generalized fractional derivative recently proposed by Katugampola.
Daniela S. Oliveira +1 more
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Variational Problems Involving a Caputo-Type Fractional Derivative [PDF]
, 2017 We study calculus of variations problems, where the Lagrange function depends on the Caputo-Katugampola fractional derivative. This type of fractional operator is a generalization of the Caputo and the Caputo–Hadamard fractional derivatives, with ...
Almeida, Ricardo
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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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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 +3 more
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Numerical methods for fractional differential equations by new caputo and hadamard types operators [PDF]
, 2020 Fractional ordinary differential equation (FODE) and fractional partial differential equation (FPDE) emerges in various modelling of physics phenomena. Over past decades, several fractional derivative and operator has been introduced such as Caputo-
Toh, Yoke Teng
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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 +2 more
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