On Solving Comfortable Fractional Differential Equations

Widad Raisan Khudair

On Solving Comfortable Fractional Differential Equations

Widad Raisan Khudair

Abstract

This paper adopts the relationship between conformable fractional derivative and the classical derivative. By using this relation, the comfortable fractional differential equation can transform to a classical differential equation such that the solution of these differential equations is the same. Two examples have been considered to illustrate the validity of our main results.

Keywords

Differential Equation ,Conformable Fractional Differential Equations, Conformable Fractional Derivative.

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References

K. Oldham, J. spanier, The Fractional Calculus, Academic Press, New York, 1974.

S. Samko, A. Kilbas, O. Marichev, Fractional Integrals and Derivatives, Gordon and Breach, New York, 1993.

K. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.

A. Kilbas, H. Strivatava, J. Trujillo, Theory and Application of Fractional Differential Equations, Wiley, New York, 1993.

I. Pdolubny, Fractional Differential Equations, Academic Press, New York, 1999.

R. Hilfer, Application of fractional Calculus in Physics, World Scientific Publishing Company, Singapore, 2000.

G. Zaslavsky, Hamiltonian Chaos and Fractional Dynamics, Oxford University Press, Oxford, 2005.

W. Schneider and W. Wyss, Fractional diffusion and wave equations, J Math Phys 30 (1), 1989, 134–144.

R. Gorenflo and F. Mainardi, Fractional calculus, 1997, Springer

R.L. Magin, C. Ingo, L. Colon-Perez, W. Triplett and T.H. Mareci, Characterization of anomalous diffusion in porous biological tissues using fractional order derivatives and entropy, Microporous Mesoporous

Mater 178, 2013, 39–43.

R.L. Magin, Fractional calculus models of complex dynamics in biological tissues, Comput Math Appl 59 (5), 2010, 1586–1593.

R. Metzler and J. Klafter, Boundary value problems for fractional diffusion equations, Physica A 278 (1), 2000, 107–125.

H. Beyer, S. Kempfle, Definition of physically consistent damping laws with fractional derivatives, ZAMM-J Appl Math Mech/Zeitschrift fÄur Angewandte Mathematik und Mechanik 75 (8) (1995)

–635.

W. Lederman and Roquejoffre, Mathematical justification of a nonlinear integrodifferential equation for the propagation of spherical flames, Ann di Mate 183, 2004, 173–239.

P.J. Torvik and R.L. Bagley, On the appearance of the fractional derivative in the behavior of real materials, J Appl Mech 51 (2), 1984, 294–298.

F. Riewe, Nonconservative Lagrangian and Hamiltonian mechanics, Phys Rev E 53 (2), 1996, 1890.

V.V. Kulish and J.L. Lage, Application of fractional calculus to fluid mechanics, J Fluids Eng 124 (3), 2002, 803–806.

W. Wyss, The fractional Black–Scholes equation, Fractional Calculus Appl Anal 3 (1), 2000, 51–62.

L. Song and W. Wang, Solution of the fractional Black–Scholes option pricing model by finite difference method, Abstr. Appl. Anal 2013, 2013, Hindawi Publishing Corporation.

F. Keil, W. Mackens, H. VoB and J. Werther, Scientific computing in chemical engineering II: computational fluid dynamics, reaction engineering, and molecular properties, 2012, Springer Science & Business Media.

R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math. 264 (2014) 6570.

E. Unal, A. Gokdogan I. Cumhur, The operator method for local fractional linear differential equations, Vol. 131, (2017), 986-993.

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