The use of partition polynomial series in Laplace inversion of composite functions with applications in fractional calculus

This paper is dealing the modified Ohm's law with the temperature gradient of generalized theory of magneto-thermo-viscoelastic for a thermally, isotropic and electrically infinite material with a spherical region using fractional order derivative. The general solution obtained from Laplace transform, numerical Laplace inversion and state space approach. The temperature, displacement and stresses are obtained and represented graphically with the help of Mathcad software.

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A note on fractional integral operator associated with multiindex Mittag-Leffler functions

Filomat ◽

10.2298/fil1607931c ◽

2016 ◽

Vol 30 (7) ◽

pp. 1931-1939 ◽

Cited By ~ 19

Author(s):

Junesang Choi ◽

Praveen Agarwal

Keyword(s):

Integral Operator ◽

Fractional Calculus ◽

Fractional Integral ◽

Fractional Integration ◽

Fractional Integral Operator ◽

Integration Formula ◽

Special Cases

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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