Results in Physics, 2021 This paper is concerned to present and apply a new generalized fractional derivative, that is the Generalized Hilfer-type (GH) fractional derivative.
Tahir Ullah Khan +2 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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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 +5 more
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On Caputo fractional derivative inequalities by using strongly (α,h−m)-convexity
AIMS Mathematics, 2022 In the literature of mathematical inequalities, one can have different variants of the well-known Hadamard inequality for CFD (Caputo fractional derivatives).
Tao Yan +3 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 +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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The Allen-Cahn equation with a time Caputo-Hadamard derivative: Mathematical and Numerical Analysis
Communications in Analysis and Mechanics, 2023 In this paper, we investigate the local discontinuous Galerkin (LDG) finite element method for the fractional Allen-Cahn equation with Caputo-Hadamard derivative in the time domain.
Zhen Wang, Luhan Sun
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Some new Caputo fractional derivative inequalities for exponentially (θ,h−m)–convex functions
AIMS Mathematics, 2022 Firstly, we obtain some inequalities of Hadamard type for exponentially (θ,h−m)–convex functions via Caputo k–fractional derivatives. Secondly, using integral identity including the (n+1)–order derivative of a given function via Caputo k-fractional ...
Imran Abbas Baloch +5 more
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Existence criteria for fractional differential equations using the topological degree method
AIMS Mathematics, 2023 In this work, we analyze the fractional order by using the Caputo-Hadamard fractional derivative under the Robin boundary condition. The topological degree method combined with the fixed point methodology produces the desired results. Finally to show how
Kottakkaran Sooppy Nisar +5 more
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Inequalities for different type of functions via Caputo fractional derivative
AIMS Mathematics, 2022 In this paper, we obtain some new inequalities for different type of functions that are connected with the Caputo fractional derivative. We extend and generalize some important inequalities to this interesting calculus including Hermite-Hadamard ...
Deniz Uçar
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