Results 1 to 10 of about 545,475 (201)
On an extension of Hadamard fractional derivative [PDF]
Journal of Inequalities and Applications, 2019 In this paper, we introduce a new approach to the fractional derivation which generalizes the classical Hadamard fractional derivative. We prove some properties of this new approach and also establish some results by addressing some standard functions.
Muhammad Samraiz +2 more
exaly +4 more sources
Logarithmic Bernstein functions for fractional Rosenau–Hyman equation with the Caputo–Hadamard derivative [PDF]
Results in PhysicsIn this study, the Caputo–Hadamard derivative is fittingly used to define a fractional form of the Rosenau–Hyman equation. To solve this equation, the orthonormal logarithmic Bernstein functions (BFs) are created as a suitable basis for handling this ...
Mohammad Hossein Heydari +2 more
exaly +5 more sources
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
doaj +2 more sources
Hadamard-Type Fractional Heat Equations and Ultra-Slow Diffusions
Fractal and Fractional, 2021 In this paper, we study diffusion equations involving Hadamard-type time-fractional derivatives related to ultra-slow random models. We start our analysis using the abstract fractional Cauchy problem, replacing the classical time derivative with the ...
Alessandro De Gregorio, Roberto Garra
doaj +3 more sources
Journal of Inequalities and Applications, 2021 In this work, we establish Lyapunov-type inequalities for the fractional boundary value problems with Caputo–Hadamard fractional derivative subject to multipoint and integral boundary conditions. As far as we know, there is no literature that has studied
Youyu Wang
exaly +2 more sources
Existence Results for Caputo–Hadamard Nonlocal Fractional Multi-Order Boundary Value Problems [PDF]
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
doaj +3 more sources
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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Mathematics, 2021 In the finance market, it is well known that the price change of the underlying fractal transmission system can be modeled with the Black-Scholes equation.
Sivaporn Ampun, Panumart Sawangtong
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Existence and Uniqueness of Generalised Fractional Cauchy-Type Problem
Universal Journal of Mathematics and Applications, 2020 In this paper, we study the existence and uniqueness of Generalized Fractional Cauchy-type problem involving Hilfer-Hadamard-type fractional derivative for a nonlinear fractional differential equation.
Ahmad Y. A. Salamoonı, D.d. Pawar
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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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