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Volume 13 / No 1 (2018)

Mathematical Modelling of Natural Phenomena

Volume 13 / No 1 (2018)

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Theory and applications of fractional differentiation

Application of Atangana-Baleanu fractional derivative to convection flow of MHD Maxwell fluid in a porous medium over a vertical plate 1

K.A. Abro, I. Khan and A. Tassaddiq

Published online: 06 April 2018

DOI: https://doi.org/10.1051/mmnp/2018007

Applications of fractional derivatives to nanofluids: exact and numerical solutions 2

Sidra Aman, Ilyas Khan, Zulkhibri Ismail and Mohd Zuki Salleh

Published online: 06 April 2018

DOI: https://doi.org/10.1051/mmnp/2018013

New numerical approach for fractional differential equations 3

Abdon Atangana and Kolade M. Owolabi

Published online: 06 April 2018

DOI: https://doi.org/10.1051/mmnp/2018010

A reliable mixed method for singular integro-differential equations of non-integer order 4

Dumitru Baleanu, Rahmat Darzi and Bahram Agheli

Published online: 26 February 2018

DOI: https://doi.org/10.1051/mmnp/2018011

Reconstruction of the Robin boundary condition and order of derivative in time fractional heat conduction equation 5

Rafał Brociek and Damian Słota

Published online: 06 April 2018

DOI: https://doi.org/10.1051/mmnp/2018008

Fourth-order fractional diffusion model of thermal grooving: integral approach to approximate closed form solution of the Mullins model 6

Jordan Hristov

Published online: 06 April 2018

DOI: https://doi.org/10.1051/mmnp/2017080

Numerical approach to fractional blow-up equations with Atangana-Baleanu derivative in Riemann-Liouville sense 7

Kolade M. Owolabi

Published online: 26 February 2018

DOI: https://doi.org/10.1051/mmnp/2018006

Exact solutions for the blood flow through a circular tube under the influence of a magnetic field using fractional Caputo-Fabrizio derivatives 8

M.B. Riaz and A.A. Zafar

Published online: 26 February 2018

DOI: https://doi.org/10.1051/mmnp/2018005

Uniform asymptotic stability of a fractional tuberculosis model 9

Weronika Wojtak, Cristiana J. Silva and Delfim F.M. Torres

Published online: 06 April 2018

DOI: https://doi.org/10.1051/mmnp/2018015

Fractional compound Poisson processes with multiple internal states 10

Pengbo Xu and Weihua Deng

Published online: 06 April 2018

DOI: https://doi.org/10.1051/mmnp/2018001

Well-posedness of the time-space fractional stochastic Navier-Stokes equations driven by fractional Brownian motion 11

Pengfei Xu, Caibin Zeng and Jianhua Huang

Published online: 06 April 2018

DOI: https://doi.org/10.1051/mmnp/2018003

A different approach to the European option pricing model with new fractional operator 12

M. Yavuz and N. Özdemir

Published online: 06 April 2018

DOI: https://doi.org/10.1051/mmnp/2018009

Numerical and analytical solutions of nonlinear differential equations involving fractional operators with power and Mittag-Leffler kernel 13

H. Yépez-Martínez and J.F. Gómez-Aguilar

Published online: 26 February 2018

DOI: https://doi.org/10.1051/mmnp/2018002

First integral method for non-linear differential equations with conformable derivative 14

H. Yépez-Martínez, J.F. Gómez-Aguilar and Abdon Atangana

Published online: 26 February 2018

DOI: https://doi.org/10.1051/mmnp/2018012

Existence and regularity of mild solutions to fractional stochastic evolution equations 15

G.A. Zou, B. Wang and Y. Zhou

Published online: 26 February 2018

DOI: https://doi.org/10.1051/mmnp/2018004