A new conformal fractional integrals and derivatives
DOI :
https://doi.org/10.5269/bspm.77933Résumé
In this work, a new definition of conformal fractional integrals and derivatives are defined by another function $h(x)$, namely $\alpha$-M-conformal fractional derivative and $\alpha$-M-conformal fractional integral as generalized for some types of conformal fractional derivative and integral. This type of conformal fractional obeys classical properties like linearity, power rule, chain rule, product and quotient rule.
Références
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8. Geem M. H. , On strongly continuous Ïh-semigroup, in Journal of Physics: Conference Series, 2019, vol. 1234, no. 1: IOP Publishing.
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11. Geem M.H. ,Hassan, Ahmed Raad and Neamah, Hayder Ismael,0-Semigroup of g-transformation,Journal of Interdisciplinary Mathematics, vol.28:1,2025, pp.311–316, DOI: 10.47974/JIM-1986
12. Iqbal S. , S. Mubeen, and M. Tomar, On Hadamard k-fractional integrals J. Fract. Calc. Appl, vol. 9, no. 2, pp. 255-267, 2018.
13. Ji S. and D. Yang, Solutions to Riemann–Liouville fractional integrodifferential equations via fractional resolvents Advances in Difference Equations, vol. 2019, no. 1, p. 524, 2019.
14. Kilbas A. A. , H. M. Srivastava, and J. J. Trujillo,Theory and applications of fractional differential equations. elsevier, 2006.
15. Kilbas R. Khalil, M. Al Horani, A. Yousef, and M. Sababheh, A new definition of fractional derivative Journal of Computational and Applied Mathematics, vol. 264, pp. 65–70, 2014.
16. KOCHUBEI A. ,Handbook of fractional calculus with applications. Berlin: Gruter, 2019.
17. Katugampola U. N. , New approach to a generalized fractional integral Applied mathematics and computation, vol. 218, no. 3, pp. 860-865, 2011.
18. Oliveira D. S. and E. Capelas de Oliveira, On a Caputo-type fractional derivative,” Advances in Pure and Applied Mathematics, vol. 10, no. 2, pp. 81-91, 2019.
19. AL-Ameri Y., M. H. Geem, On g-transformation, Journal of university of Babylon,Pure and applied sciences, Vol29,2021.
2. Almeida R., A. B. Malinowska, and M. T. T. Monteiro, Fractional differential equations with a Caputo derivative with respect to a kernel function and their applications, Mathematical Methods in the Applied Sciences, vol. 41, no. 1, pp. 336-352, 2018.
3. Caozong C., Ton J., Fractional boundary value problems with Riemann-Liouville fractional derivatives, Advances in Difference Equations, 2015, pp. 1-80.
4. Balachandran K. , M. Matar, N. Annapoorani, and D. Prabu, Hadamard functional fractional integrals and derivatives and fractional differential equations, Filomat, vol. 38, no. 3, pp. 779-792, 2024.
5. Balachandran K. , An introduction to fractional differential equations. Singapore: Springer, 2023
6. Farid G. , F. Rehman, Z. Javid, K. Shahzadi, A. Javed, and M. Ghamkhar, Some New Fractional Integrals And Their Semigroup Properties, Migration Letters, vol. 21, no. S11, pp. 1159-1168, 2024.
7. Hassan S.M., D.M. Hamid, M.H. Geem , A Novel Approach using Residual Power series Method for solving nonlinear fractional partial differential equation, submitted on journal the Bulletin of Paranás Mathematical Society, named Boletim da Sociedade Paranaense de Matematica (BSPM), 2025.
8. Geem M. H. , On strongly continuous Ïh-semigroup, in Journal of Physics: Conference Series, 2019, vol. 1234, no. 1: IOP Publishing.
9. Geem M. H. and A. M. Abbood, On α-g-Transformation and its properties, in American Institute of Physics Conference Series, 2023, vol. 2834, no. 1, p. 080103.
10. Hassan, S.M., Hamid, D.M. and Geem M.H., A Novel Approach using Residual Power series Method for solving nonlinear fractional partial differential equation, in Boletim Da Sociedade Paranaense De MatematicaOpen, 2025, vol. 43, no. 1, pp. 1-5.
11. Geem M.H. ,Hassan, Ahmed Raad and Neamah, Hayder Ismael,0-Semigroup of g-transformation,Journal of Interdisciplinary Mathematics, vol.28:1,2025, pp.311–316, DOI: 10.47974/JIM-1986
12. Iqbal S. , S. Mubeen, and M. Tomar, On Hadamard k-fractional integrals J. Fract. Calc. Appl, vol. 9, no. 2, pp. 255-267, 2018.
13. Ji S. and D. Yang, Solutions to Riemann–Liouville fractional integrodifferential equations via fractional resolvents Advances in Difference Equations, vol. 2019, no. 1, p. 524, 2019.
14. Kilbas A. A. , H. M. Srivastava, and J. J. Trujillo,Theory and applications of fractional differential equations. elsevier, 2006.
15. Kilbas R. Khalil, M. Al Horani, A. Yousef, and M. Sababheh, A new definition of fractional derivative Journal of Computational and Applied Mathematics, vol. 264, pp. 65–70, 2014.
16. KOCHUBEI A. ,Handbook of fractional calculus with applications. Berlin: Gruter, 2019.
17. Katugampola U. N. , New approach to a generalized fractional integral Applied mathematics and computation, vol. 218, no. 3, pp. 860-865, 2011.
18. Oliveira D. S. and E. Capelas de Oliveira, On a Caputo-type fractional derivative,” Advances in Pure and Applied Mathematics, vol. 10, no. 2, pp. 81-91, 2019.
19. AL-Ameri Y., M. H. Geem, On g-transformation, Journal of university of Babylon,Pure and applied sciences, Vol29,2021.
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Publié
2025-12-19
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Special Issue: Advanced Computational Methods for Fractional Calculus
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