TY - GEN
T1 - Elimination of the Nondifferentiation Problem and the Discontinuity Problem by the Conformable Definition.
AU - Aljazzazi, Mazin
AU - Bouchenak, Ahmed
AU - Momani, Shaher
AU - Al-Smadi, Mohammed
N1 - Publisher Copyright:
© 2023 IEEE.
PY - 2023
Y1 - 2023
N2 - Fractional calculus is now used in a variety of domains, including physics and engineering which have two problems in their study are the differentiation and the discontinuity problems. Hence, in this paper, we will present the conformable fractional derivative and integral. Then, we will use such definition and properties to construct functions that are differentiable in a fractional meaning but not differentiable in classical meaning at the point 0, then we will develop the construction of the mentioned kind functions at any point which will eliminate the first problem. Therefore, we will eliminate the second problem by approximate any given discontinuous function by its conformable fractional Fourier series which will be continuous and useful for the study that researchers need.
AB - Fractional calculus is now used in a variety of domains, including physics and engineering which have two problems in their study are the differentiation and the discontinuity problems. Hence, in this paper, we will present the conformable fractional derivative and integral. Then, we will use such definition and properties to construct functions that are differentiable in a fractional meaning but not differentiable in classical meaning at the point 0, then we will develop the construction of the mentioned kind functions at any point which will eliminate the first problem. Therefore, we will eliminate the second problem by approximate any given discontinuous function by its conformable fractional Fourier series which will be continuous and useful for the study that researchers need.
KW - Conformable derivative
KW - Conformable integral
KW - Continuity
KW - Fourier series
KW - Usual and fractional differentiability
UR - https://www.scopus.com/pages/publications/85164534773
U2 - 10.1109/ICFDA58234.2023.10153259
DO - 10.1109/ICFDA58234.2023.10153259
M3 - Conference contribution
AN - SCOPUS:85164534773
T3 - 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023
BT - 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023
Y2 - 14 March 2023 through 16 March 2023
ER -