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2017
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1
47
The non-linear Dodson diffusion equation: Approximate solutions and beyond with formalistic fractionalization
The non-linear Dodson diffusion equation: Approximate solutions and beyond with formalistic fractionalization
en
en
The Dodson mass diffusion equation with exponentially diffusivity is analyzed through approximate integral solutions.
Integral-balance solutions were developed to integer-order versions as well as to formally fractionalized models. The formal
fractionalization considers replacement of the time derivative with a fractional version with either singular (Riemann-Liouville
or Caputo) or non-singular fading memory. The solutions developed allow seeing a new side of the Dodson equation and
to separate the formal fractional model with Caputo-Fabrizio time derivative with an integral-balance allowing relating the
fractional order to the physical relaxation time as adequate to the phenomena behind.
1
17
Jordan
Hristov
Non-linear diffusion
singular fading memory
non-singular fading memory
formal fractionalization
integral balance approach
Article.1.pdf
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New direction in fractional differentiation
New direction in fractional differentiation
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en
Based upon the Mittag-Leffler function, new derivatives with fractional order were constructed. With the same line of
idea, improper derivatives based on the Weyl approach are constructed in this work. To further model some complex physical
problems that cannot be modeled with existing derivatives with fractional order, we propose, a new derivative based on the
more generalized Mittag-Leffler function known as Prabhakar function. Some new results are presented together with some
applications.
18
25
Abdon
Atangana
Ilknur
Koca
Atangana-Baleanu fractional derivatives
Weyl approach
Prabhakar Mittag-Leffler function
integral transform
Article.2.pdf
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Generalized fractional calculus of the multiindex Bessel function
Generalized fractional calculus of the multiindex Bessel function
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en
The present paper is devoted to the study of the fractional calculus operators to obtain a number of key results for the
generalized multiindex Bessel function involving Saigo hypergeometric fractional integral and differential operators in terms
of generalized Wright function. Various particular cases and consequences of our main fractional-calculus results as classical
Riemann-Liouville and Erde´lyi-Kober fractional integral and differential formulas are deduced.
26
32
D. L.
Suthar
S. D.
Purohit
R. K.
Parmar
Fractional calculus operators
multiindex Bessel function
Wright function.
Article.3.pdf
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A uniqueness theorem for eigenvalue problem having special potential type
A uniqueness theorem for eigenvalue problem having special potential type
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en
In this study, a uniqueness theorem is given for
Sturm-Liouville problem with special singular potential. We prove that
singular potential function can be uniquely determined by the spectral set \(
\left\{ \lambda _{n}\left( q_{0},h_{m}\right) \right\} _{m=1}^{+\infty }.\)
33
39
Erdal
Bas
Etibar S.
Panakhov
Resat
Yilmazer
Singular
Sturm Liouville
uniqueness theorem
eigenvalue
Article.4.pdf
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Stochastic fixed point theorems for a random Z-contraction in a complete probability measure space with application to non-linear stochastic integral equations
Stochastic fixed point theorems for a random Z-contraction in a complete probability measure space with application to non-linear stochastic integral equations
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en
In this paper, we propose the random \(\mathcal{Z}\)-contraction, prove a stochastic fixed point theorem for this contraction, and show that a solution for a non-linear stochastic integral equations exists in Banach spaces.
40
48
Plern
Saipara
Poom
Kumam
Apirak
Sombat
Anantachai
Padcharoen
Wiyada
Kumam
\(\mathcal{Z}\)-contraction
stochastic fixed point theorem
complete probability measure spaces
Article.5.pdf
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