Newly Defined Conformable Derivatives

By Douglas R. Anderson, Darin J. Ulness. 2015

231 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/e4aa519bd4be3708ebefdd4917a418e0fa7f2efd

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Citations in the corpus

More properties of the proportional fractional integrals and derivatives of a function with respect to another function (2020, background): “1 (Modified conformable derivatives; [22, 23]) For ∈ [0, 1], let the functions κ0,κ1 : [0, 1] ×R → [0,∞) be continuous such that for all t ∈R we have”
On more general forms of proportional fractional operators (2019, methodology): “Motivated by the above mentioned background, we extend the work done in [23] introduce a new generalized fractional calculus based on the proportional derivatives of a function with respect to another function in paralel with the definition discussed in [21].”
Applying new fixed point theorems on fractional and ordinary differential equations (2019, background): “1) is the fractional derivative that was found together with its discrete version in [2] and [3] in an attempt to find the fractional operators generated by the local proportional derivative proposed in [36] as a modified version of the conformable derivative [37, 38].”
On a Fractional Operator Combining Proportional and Classical Differintegrals (2020, methodology): “Furthermore, we recall from [15] the following general non-fractional differential operator, which has been called “proportional” or “conformable”: Dα f (t) = K1(α, t) f (t) + K0(α, t) f ′(t),”
Certain inequalities via generalized proportional Hadamard fractional integral operators (2019, background): “Later on in [12], Anderson and Unless improved the idea of the fractional conformable derivative by introducing the idea of local proportional derivatives.”
Novel solution methods for initial boundary value problems of fractional order with conformable differentiation (2017, background): “Recently, [20-22] introduced a new fractional derivative called conformable derivative operator (CDO) and by the help of this operator, the behaviors of many scientific problems have been solved and some solution methods have been developed.”