Ünal, Emrah; Gökdoğan, Ahmet

Recently, a new fractional derivative called the conformable fractional derivative is given which is based on the basic limit definition of the derivative in (Khalil et al., 2014). Then, the fractional versions of chain rules, exponential functions, Gronwall's inequality, integration by parts, Taylor power series expansions is developed in (Abdeljawad, 2015). In this paper, we give conformable fractional differential transform method and its application to conformable fractional differential equations.

Ünal, Emrah; Gökdoğan, Ahmet; Cumhur, İshak

In this work, we give the particular solution for nonhomogeneous sequential linear conformable fractional differential equations with constant coefficients by using the operator method.

Gökdoğan, Ahmet; Ünal, Emrah

In this work, we give the fractional power series solutions around = 0 -ordinary point of conformable fractional first and second kind Chebyshev differential equations. We present first and second kind fractional Chebyshev polynomials using by these solutions. Finally, we present certain property of fractional first and second kind Chebyshev polynomials.

Gökdoğan, Ahmet; Ünal, Emrah; Çelik, Ercan

Recently, a new definition of fractional derivative called as the conformable fractional derivative which based on limits introduced by Khalil et al (2014). Later, Abdeljawad (2015) improved these definitions and gave the basic concepts in this new fractional calculus. In this paper, we generalize Abel's formula and Wronskian determinant definition and establish existence and uniqueness theorems for sequential linear conformable fractional differential equations.

Ünal, Emrah; Yalçin, Numan; Çelik, Ercan; Ashyralyev, A; Malkowsky, E

In this paper, Hartley series are presented first. Then, the operational matrix of integration together with the product and coefficient matrices are presented. They are used to transform linear differential equation systems to a set of linear algebraic equations. Finally, numerical examples are given.