Caputo-Hadamard fractional differential equations on time scales: Numerical scheme, asymptotic stability, and chaos.
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DOI: 10.1063/5.0098375
Abstract: This study investigates Caputo-Hadamard fractional differential equations on time scales. The Hadamard fractional sum and difference are defined for the first time. A general logarithm function on time scales is used as a kernel function.… read more here.
Keywords: time; hadamard fractional; caputo hadamard; time scales ... See more keywords
On Caputo–Hadamard fractional differential equations
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DOI: 10.1080/00207160.2019.1626012
Abstract: ABSTRACT In this paper, the existence and uniqueness of solution to Caputo–Hadamard fractional differential equation (FDE) are studied. The continuation theorem is established too. Then, Euler and predictor–corrector methods are built up to solve Caputo–Hadamard… read more here.
Keywords: hadamard fractional; caputo hadamard; fractional differential; differential equations ... See more keywords
A wavelet method for solving Caputo–Hadamard fractional differential equation
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DOI: 10.1108/ec-03-2021-0165
Abstract: PurposeThe purpose of the present work is to propose a wavelet method for the numerical solutions of Caputo–Hadamard fractional differential equations on any arbitrary interval.Design/methodology/approachThe author has modified the CAS wavelets (mCAS) and utilized it… read more here.
Keywords: hadamard fractional; method; fractional differential; author ... See more keywords
THE HADAMARD FRACTIONAL CALCULUS OF A FRACTAL FUNCTION
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DOI: 10.1142/s0218348x18500251
Abstract: This paper investigates the Hadamard fractional calculus of a fractal function. It is proved that there exists some linear relationship between the order of Hadamard fractional calculus and the fra... read more here.
Keywords: hadamard fractional; calculus fractal; fractional calculus; fractal function ... See more keywords
The General Solution of Differential Equations with Caputo-Hadamard Fractional Derivatives and Noninstantaneous Impulses
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DOI: 10.1155/2017/3094173
Abstract: Based on some recent works about the general solution of fractional differential equations with instantaneous impulses, a Caputo-Hadamard fractional differential equation with noninstantaneous impulses is studied in this paper. An equivalent integral equation with some… read more here.
Keywords: hadamard fractional; general solution; differential equations; caputo hadamard ... See more keywords
On a fractional Caputo–Hadamard problem with boundary value conditions via different orders of the Hadamard fractional operators
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DOI: 10.1186/s13662-020-02741-7
Abstract: We investigate the existence of solutions for a Caputo–Hadamard fractional integro-differential equation with boundary value conditions involving the Hadamard fractional operators via different orders. By using the Krasnoselskii’s fixed point theorem, the Leray–Schauder nonlinear alternative,… read more here.
Keywords: hadamard fractional; via different; fractional operators; boundary value ... See more keywords
Eigenvalue problems for a class of nonlinear Hadamard fractional differential equations with p-Laplacian operator
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DOI: 10.1515/ms-2017-0336
Abstract: Abstract This paper is concerned with the existence and nonexistence of positive solutions for the eigenvalue problems of nonlinear Hadamard fractional differential equations with p-Laplacian operator. By applying the properties of the Green function and… read more here.
Keywords: hadamard fractional; equations laplacian; eigenvalue problems; fractional differential ... See more keywords
Positive solutions for a class of nonlinear p-Laplacian Hadamard fractional differential systems with coupled nonlocal Riemann-Stieltjes integral boundary conditions
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DOI: 10.2298/fil2219631y
Abstract: This paper investigates a class of nonlinear p-Laplacian Hadamard fractional differential systems with coupled nonlocal Riemann-Stieltjes integral boundary conditions. First, we obtain the corresponding Green?s function for the considered boundary value problems and some of… read more here.
Keywords: class nonlinear; differential systems; laplacian hadamard; hadamard fractional ... See more keywords
Random Coupled Hilfer and Hadamard Fractional Differential Systems in Generalized Banach Spaces
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DOI: 10.3390/math7030285
Abstract: This article deals with some existence and uniqueness result of random solutions for some coupled systems of Hilfer and Hilfer–Hadamard fractional differential equations with random effects. Some applications are made of generalizations of classical random… read more here.
Keywords: fractional differential; generalized banach; hilfer hadamard; hadamard fractional ... See more keywords