On conformable fractional calculus

Summary

The basic concepts in this new simple interesting fractional calculus called conformable fractional derivative are set and the fractional versions of chain rule, exponential functions, Gronwall's inequality, integration by parts, Taylor power series expansions, Laplace transforms and linear differential systems are proposed and discussed.

Keywords

Conformable matrix, Mathematics, Fractional calculus, Laplace transform, Calculus (dental)

References

Fractional Integrals and Derivatives: Theory and ApplicationsStefan Samko, Anatoly A. Kilbas, O. I. Marichev — 1993
Initial value problems in discrete fractional calculusFerhan M. Atıcı, Paul W. Eloe — 2008
On a new definition of the fractional differenceH. L. Gray, Nien Fan Zhang — 1988
On the Definitions of Nabla Fractional OperatorsThabet Abdeljawad, Ferhan M. Atıcı — 2012
A new definition of fractional derivativeRoshdi Khalil, Mohammed Al Horani, A. Yousef — 2014
Dual identities in fractional difference calculus within RiemannThabet Abdeljawad — 2011
Fractional Differential EquationsT. Kaczorek, K. Rogowski — 2015

Cited by

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A Conformable Fractional Calculus on Arbitrary Time ScalesNadia Benkhettou, Salima Hassani, Delfim F. M. Torres — 2015
Properties of the Katugampola fractional derivative with potential application in quantum mechanicsDouglas R. Anderson, Darin J. Ulness — 2015
Existence and Uniqueness Theorems for Sequential Linear Conformable Fractional Differential EquationsAhmet Gökdoğan, Emrah Ünal, Ercan Çeli̇k — 2015
Solutions of Sequential Conformable Fractional Differential Equations around an Ordinary Point and Conformable Fractional Hermite Differential EquationEmrah Ünal, Ahmet an, Ercan Çeli̇k — 2015
Numerical solution of multi-order fractional differential equations via the sinc collocation methodEsmail Hesameddini, Elham Asadollahifard — 2015
ABEL'S FORMULA AND WRONSKIAN FOR CONFORMABLE FRACTIONAL DIFFERENTIAL EQUATIONSMALIKA HAMMAD, Roshdi Khalil — 2014
What is a fractional derivative?Manuel Duarte Ortigueira, J. A. Tenreiro Machado — 2015
Legendre fractional differential equation and Legender fractional polynomialsRoshdi Khalil, Mamoon Abu Hammad — 2014
On a generalized Laplace transformRoop Narain — 1958
Solutions for Space–Time Fractional (2 + 1)-Dimensional Dispersive Long Wave EquationsMostafa Eslami — 2016
Existence of solution to a local fractional nonlinear differential equationBenaoumeur Bayour, Delfim F. M. Torres — 2016
General Solution to Sequential Linear Conformable Fractional Differential Equations With Constant CoefficientsEmrah Ünal, Ahmet Gökdoğan, Ercan Çeli̇k — 2016
Conformable Fractional Bessel Equation and Bessel FunctionsAhmet Gökdoğan, Emrah Ünal, Ercan Çeli̇k — 2015
Solutions around a Regular α Singular Point of a Sequential Conformable Fractional Differential EquationEmrah Ünal, Ahmet Gökdoğan, Ercan Çeli̇k — 2015
New soliton solutions to the fractional perturbed nonlinear Schrodinger equation with power law nonlinearityAhmad Neirameh — 2016
A New fractional derivative for differential equation of fractional order under interval uncertaintySoheil Salahshour, Ali Ahmadian, Fudzial Ismail — 2015
The first integral method for Wu–Zhang system with conformable time-fractional derivativeMostafa Eslami, Hadi Rezazadeh — 2016
On geometric fractional calculusThabet Abdeljawad, Michael Grossman — 2016
Estimation of Unknown Function of a Class of Nonlinear Weakly Singular Integral InequalityChunmiao Huang, Wu-Sheng Wang — 2015

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