Fractional Calculus in Bioengineering, Part 1

Recently Kiryakova and several other ones have investigated so-called multiindex Mittag-Leffler functions associated with fractional calculus. Here, in this paper, we aim at establishing a new fractional integration formula (of pathway type) involving the generalized multiindex Mittag-Leffler function E?,k[(?j,?j)m;z]. Some interesting special cases of our main result are also considered and shown to be connected with certain known ones.

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A remark on local fractional calculus and ordinary derivatives

Open Mathematics ◽

10.1515/math-2016-0104 ◽

2016 ◽

Vol 14 (1) ◽

pp. 1122-1124 ◽

Cited By ~ 12

Author(s):

Ricardo Almeida ◽

Małgorzata Guzowska ◽

Tatiana Odzijewicz

Keyword(s):

Fractional Calculus ◽

Fractional Derivative ◽

Short Note ◽

General Definition ◽

Local Fractional Derivative ◽

Fundamental Properties ◽

Local Fractional Calculus ◽

Definition Of

AbstractIn this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new concept and ordinary differentiation. Using such formula, most of the fundamental properties of the fractional derivative can be derived directly.

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Coulostatics in bioelectrochemistry: A physical interpretation of the electrode-tissue processes from the theory of fractional calculus

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2021.110787 ◽

2021 ◽

Vol 145 ◽

pp. 110787

Author(s):

E. Hernández-Balaguera

Keyword(s):

Fractional Calculus ◽

Physical Interpretation

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On the fractional calculus of multivariate Mittag-Leffler functions

International Journal of Computer Mathematics ◽

10.1080/00207160.2021.1906869 ◽

2021 ◽

pp. 1-30

Author(s):

Mehmet Ali Özarslan ◽

Arran Fernandez

Keyword(s):

Fractional Calculus

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The memory effect on fractional calculus: an application in the spread of COVID-19

Computational and Applied Mathematics ◽

10.1007/s40314-021-01456-z ◽

2021 ◽

Vol 40 (3) ◽

Author(s):

Laécio Carvalho de Barros ◽

Michele Martins Lopes ◽

Francielle Santo Pedro ◽

Estevão Esmi ◽

José Paulo Carvalho dos Santos ◽

...

Keyword(s):

Fractional Calculus ◽

Memory Effect

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New fractional approaches for n-polynomial P-convexity with applications in special function theory

Advances in Difference Equations ◽

10.1186/s13662-020-03000-5 ◽

2020 ◽

Vol 2020 (1) ◽

Cited By ~ 1

Author(s):

Shu-Bo Chen ◽

Saima Rashid ◽

Muhammad Aslam Noor ◽

Zakia Hammouch ◽

Yu-Ming Chu

Keyword(s):

Fractional Calculus ◽

Convex Functions ◽

Special Functions ◽

Real Life ◽

Fractional Integrals ◽

Digamma Function ◽

Novel Approach ◽

Inequality Theory ◽

New Strategy ◽

Significant Mechanism

Abstract Inequality theory provides a significant mechanism for managing symmetrical aspects in real-life circumstances. The renowned distinguishing feature of integral inequalities and fractional calculus has a solid possibility to regulate continuous issues with high proficiency. This manuscript contributes to a captivating association of fractional calculus, special functions and convex functions. The authors develop a novel approach for investigating a new class of convex functions which is known as an n-polynomial $\mathcal{P}$ P -convex function. Meanwhile, considering two identities via generalized fractional integrals, provide several generalizations of the Hermite–Hadamard and Ostrowski type inequalities by employing the better approaches of Hölder and power-mean inequalities. By this new strategy, using the concept of n-polynomial $\mathcal{P}$ P -convexity we can evaluate several other classes of n-polynomial harmonically convex, n-polynomial convex, classical harmonically convex and classical convex functions as particular cases. In order to investigate the efficiency and supremacy of the suggested scheme regarding the fractional calculus, special functions and n-polynomial $\mathcal{P}$ P -convexity, we present two applications for the modified Bessel function and $\mathfrak{q}$ q -digamma function. Finally, these outcomes can evaluate the possible symmetric roles of the criterion that express the real phenomena of the problem.

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Some Applications of the Wright Function in Continuum Physics: A Survey

Mathematics ◽

10.3390/math9020198 ◽

2021 ◽

Vol 9 (2) ◽

pp. 198

Author(s):

Yuriy Povstenko

Keyword(s):

Heat Conduction ◽

Fractional Calculus ◽

Exponential Function ◽

Nonlocal Elasticity ◽

Bessel Functions ◽

Wright Function ◽

Mainardi Function ◽

Integral Relations

The Wright function is a generalization of the exponential function and the Bessel functions. Integral relations between the Mittag–Leffler functions and the Wright function are presented. The applications of the Wright function and the Mainardi function to description of diffusion, heat conduction, thermal and diffusive stresses, and nonlocal elasticity in the framework of fractional calculus are discussed.

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