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 +2 more
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Existence Results for Caputo–Hadamard Nonlocal Fractional Multi-Order Boundary Value Problems
Mathematics, 2021 In this paper, we studied the existence results for solutions of a new class of the fractional boundary value problem in the Caputo–Hadamard settings.
Shahram Rezapour +5 more
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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 +3 more
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Stability analysis of solutions and existence theory of fractional Lagevin equation
Alexandria Engineering Journal, 2021 The present article describes fractional Langevin equations (FDEs) invloving Caputo Hadamard-derivative of independent orders connected with non-local integral and non-periodic boundary conditions.
Amita Devi +3 more
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Local density of Caputo-stationary functions in the space of smooth functions [PDF]
, 2016 We consider the Caputo fractional derivative and say that a function is Caputo-stationary if its Caputo derivative is zero. We then prove that any $C^k\big([0,1]\big)$ function can be approximated in $[0,1]$ by a a function that is Caputo-stationary in $[
Bucur, Claudia
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Combination Synchronization of Fractional Systems Involving the Caputo–Hadamard Derivative
Mathematics, 2021 The main aim of this paper is to investigate the combination synchronization phenomena of various fractional-order systems using the scaling matrix. For this purpose, the combination synchronization is performed by considering two drive systems and one ...
Abdelhameed M. Nagy +3 more
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On Some Operators Involving Hadamard Derivatives [PDF]
, 2013 In this paper we introduce a novel Mittag--Leffler-type function and study its properties in relation to some integro-differential operators involving Hadamard fractional derivatives or Hyper-Bessel-type operators.
Garra, Roberto, Polito, Federico
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Multiterm Impulsive Caputo–Hadamard Type Differential Equations of Fractional Variable Order
Axioms, 2022 In this study, we deal with an impulsive boundary value problem (BVP) for differential equations of variable fractional order involving the Caputo–Hadamard fractional derivative.
Amar Benkerrouche +3 more
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Fractional Euler-Lagrange differential equations via Caputo derivatives [PDF]
, 2011 We review some recent results of the fractional variational calculus. Necessary optimality conditions of Euler-Lagrange type for functionals with a Lagrangian containing left and right Caputo derivatives are given.
AA Kilbas +29 more
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Boundary value problem for Caputo-Hadamard fractional differential equations [PDF]
Surveys in Mathematics and its Applications, 2017 The aim of this work is to study the existence and uniqueness solutions for boundary value problem of nonlinear fractional differential equations with Caputo-Hadamard derivative in bounded domain.
Yacine Arioua , Nouredine Benhamidouche
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