| Autors: Lazarević, M.P., Rapaić, M.R., Šekara, T.B., Mladenov, V. M., Mastorakis, N. Title: Introduction to fractional calculus with brief historical background Keywords: fractional calculus, historical background, Riemann-Liouvil Abstract: The Fractional Calculus (FC) is a generalization of classical calculus concerned with operations of integration and differentiation of non-integer (fractional) order. The concept of fractional operators has been introduced almost simultaneously with the development of the classical ones. The first known reference can be found in the correspondence of G. W. Leibniz and Marquis de l’Hospital in 1695 where the question of meaning of the semi-derivative has been raised. This question consequently attracted the interest of many well- known mathematicians, including Euler, Liouville, Laplace, Riemann, Grünwald, Letnikov and many others. Since the 19th century, the theory of fractional calculus developed rapidly, mostly as a foundation for a number of applied disciplines, including fractional geometry, fractional differential equations (FDE) and fractional dynamics. The applications of FC are very wide nowadays. It is safe to say that almost no discipline of modern engineering and science i References Issue
|
Цитирания (Citation/s):
1. Abuasbeh, K., Kanwal, A., Shafqat, R., Taufeeq, B., Almulla, M.A. and Awadalla, M., 2023. A method for solving time-fractional initial boundary value problems of variable order. Symmetry, vol. 15, issue (2), p.519. ISSN 20738994, DOI 10.3390/sym15020519 (Web of Science, Scopus, Google Scholar) IF 2.7, SJR 0.483 - 2023 - в издания, индексирани в Scopus или Web of Science
2. Baleanu, D., Karaca, Y., Vazquez, L. and Macias-Diaz, J.E., 2023. Advanced fractional calculus, differential equations and neural networks: analysis, modeling and numerical computations. Physica Scripta. Vol. 98, No 11, DOI 10.1088/1402-4896/acfe73 (Web of Science, Scopus, Google Scholar) IF 2.6, SJR 0.441 - 2023 - в издания, индексирани в Scopus или Web of Science
3. Nguyen, D.H., Ta, T.T., Vu, L.M., Dang, V.T., Nguyen, D.G., Le, D.T., Nguyen, D.D. and Nguyen, T.L., 2023. Fractional Order Active Disturbance Rejection Control for Canned Motor Conical Active Magnetic Bearing-Supported Pumps. Inventions, vol. 8, issue (1), p.15. ISSN 24115134, DOI 10.3390/inventions8010015 (Web of Science, Google Scholar) IF 3.4 - 2023 - в издания, индексирани в Scopus или Web of Science
4. Özyetkin, M.M. and Birdane, H., 2023. The processes with fractional order delay and PI controller design using particle swarm optimization. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), vol. 13, issue (1), pp.81-91. ISSN 21460957, DOI 10.11121/ijocta.2023.1223 (Web of Science, Scopus, Google Scholar) IF 1.6, SJR 0.352 - 2023 - в издания, индексирани в Scopus или Web of Science
5. Rasheed, S.K., Modanli, M. and Abdulazeez, S.T., 2023. STABILITY ANALYSIS AND NUMERICAL IMPLEMENTATION OF THE THIRD-ORDER FRACTIONAL PARTIAL DIFFERENTIAL EQUATION BASED ON THE CAPUTO FRACTIONAL DERIVATIVE. Journal of Applied Mathematics & Computational Mechanics, vol. 22, issue (3). ISSN 22999965, DOI 10.17512/jamcm.2023.3.03 (Web of Science, Scopus, Google Scholar) IF 1.0 - 2023 - в издания, индексирани в Scopus или Web of Science
6. Fantini, V. and Fenyes, A., 2023. Regular singular Volterra equations on complex domains. arXiv preprint arXiv:2309.00603. pp. 1 – 28, (Google Scholar) - 2023 - от чужди автори в чужди издания, неиндексирани в Scopus или Web of Science
7. Richard, T.B.F., Alain, K.S.T., Vaidyanathan, S., Clemente-Lopez, D., Munoz-Pacheco, J.M. and Martin, S.S., 2024. A fractional order HP memristive system with a line of equilibria, its bifurcation analysis, circuit simulation and ARM-FPGA-based implementation. Analog Integrated Circuits and Signal Processing, Volume 118, Issue 1, Pages 91 - 107. ISSN 09251030, DOI 10.1007/s10470-023-02199-z (Web of Science, Scopus, Google Scholar) SJR 0.332, IF 1.4 - 2024 - в издания, индексирани в Scopus или Web of Science
8. Ojo, E.K., Iyase, S.A. and Anake, T.A., 2024. Mixed fractional order p-Laplacian boundary value problem with a two-dimensional Kernel at resonance on an unbounded domain. Elsevier, Scientific African, pp. 1 - 16, ISSN 2468-2276, https://doi.org/10.1016/j.sciaf.2024. e02108. (Web of Science, Google Scholar) IF 2.9 - 2024 - в издания, индексирани в Scopus или Web of Science
9. Shafiq, F. and Malik, M., 2023. Fractional Derivatives with Applications: A Review. Mathematical Sciences and Applications, vol. 2, issue (2), pp.33-50. (Google Scholar) - 2023 - от чужди автори в чужди издания, неиндексирани в Scopus или Web of Science
10. Khurshaid, A. and Khurshaid, H., 2023. Comparative Analysis and Definitions of Fractional Derivatives. Journal ISSN, 2766, p.2276. (Google Scholar) - 2023 - от чужди автори в чужди издания, неиндексирани в Scopus или Web of Science
11. Shafique, T., Abbas, M., Mahmood, A., Abdullah, F. A., Alzaidi, A. S., & Nazir, T. (2024). “Solitary wave solutions of the fractional Peyrard Bishop DNA model,” Optical and Quantum Electronics, vol. 56, issue (5), 815. ISSN 03068919, DOI 10.1007/s11082-024-06456-x (Web of Science, Scopus, Google Scholar) SJR 0.433, IF 3.0 - 2024 - в издания, индексирани в Scopus или Web of Science
12. Adeniji, E. A., Ogundipe, S. O., Ajayi, A. A., Ojo, K. S., & Akinrinlola, S. A. (2023). “Combination-combination synchronization of chaotic fractional order systems,” Nigerian Journal of Physics, vol. 32, issue (4), pp. 57-65. DOI: https://doi.org/10.62292/njp.v32i4.2023.158 (Google Scholar) - 2023 - от чужди автори в чужди издания, неиндексирани в Scopus или Web of Science
13. Vincent Tartaglione „Analyse de la nature stochastique et modélisation interne des systèmes générant des comportements de type puissance,“ Automatique. Université de Bordeaux, 2022. Français. NNT: 2022BORD0341. (Google Scholar) - 2022 - от чужди автори в чужди издания, неиндексирани в Scopus или Web of Science
14. Ibraheem, Q.W. and Hussein, M.S., 2024, February. “Determination of time-dependent coefficient in inverse coefficient problem of fractional wave equation,” In AIP Conference Proceedings (Vol. 2922, No. 1). AIP Publishing. ISSN 0094243X, ISBN 978-073544813-1, DOI 10.1063/5.0183348 (Scopus, Google Scholar) SJR 0.164 - 2024 - в издания, индексирани в Scopus или Web of Science
15. Ali, K.K. and Maneea, M., 2023. “Optical solitons using optimal homotopy analysis method for time-fractional (1+ 1)-dimensional coupled nonlinear Schrodinger equations,” Optik, vol. 283, pp.1-15, DOI10.1016/j.ijleo.2023.170907 (Web of Science, Scopus, Google Scholar) IF 3.1 - 2023 - в издания, индексирани в Scopus или Web of Science
16. Ali, K.K., Maaty, M.A. and Maneea, M., 2023. “Optimizing option pricing: Exact and approximate solutions for the time-fractional Ivancevic model,” Alexandria Engineering Journal, vol. 84, pp.59-70. ISSN 11100168, DOI 10.1016/j.aej.2023.10.066 (Web of Science, Scopus, Google Scholar) IF 6.8, SJR 0.933 - 2023 - в издания, индексирани в Scopus или Web of Science
17. Chen, D., Anwar, M., Farid, G. and Bibi, W., 2023. “Inequalities for q-h-integrals via ℏ-convex and m-convex functions,” Symmetry, 15(3), pp. 1-10, ISSN 20738994, DOI 10.3390/sym15030666 (Web of Science, Scopus, Google Scholar) SJR 0.483, IF 2.7 - 2023 - в издания, индексирани в Scopus или Web of Science
18. Ali, K.K., Maneea, M. and Mohamed, M.S., 2023. “Solving nonlinear fractional models in superconductivity using the q-Homotopy analysis transform method,” Journal of Mathematics, 2023, pp.1-23. ISSN 23144629, DOI 10.1155/2023/6647375 (Web of Science, Scopus, Google Scholar) SJR 0.271, IF 1.4 - 2023 - в издания, индексирани в Scopus или Web of Science
19. Alsallami, S.A., Maneea, M., Khalil, E.M., Abdel-Khalek, S. and Ali, K.K., 2023. “Insights into time fractional dynamics in the Belousov-Zhabotinsky system through singular and non-singular kernels,” Scientific Reports, vol. 13, issue (1), pp. 1-19, ISSN 20452322, DOI 10.1038/s41598-023-49577-1 (Scopus, Google Scholar) SJR 0.973, IF 4.9 - 2023 - в издания, индексирани в Scopus или Web of Science
20. Usman, M., Khan, H.U., Khan, Z.A. and Alrabaiah, H., 2023. “Study of nonlinear generalized Fisher equation under fractional fuzzy concept,” AIMS Mathematics, vol. 8, issue (7), pp.16479-16493. ISSN 24736988, DOI 10.3934/math.2023842 (Web of Science, Scopus, Google Scholar) IF 2.2, SJR 0.455 - 2023 - в издания, индексирани в Scopus или Web of Science
21. Molla, M.A.K. and Mallik, S.H., 2023. “Variational principle, uniqueness and reciprocity theorems for higher order time-fractional four-phase-lag generalized thermoelastic diffusion model,” Mechanics Based Design of Structures and Machines, vol. 51, issue (4), pp.1904-1919. ISSN 15397734, DOI 10.1080/15397734.2021.1882311 (Web of Science, Scopus, Google Scholar) SJR 0.646, IF 3.9 - 2023 - в издания, индексирани в Scopus или Web of Science
22. Saidi, A., Yahya, A.M., Abouelregal, A.E., Dargail, H.E., Ahmed, I.E., Ali, E. and Mohammed, F.A., 2023. “Generalized Thermoelastic Heat Conduction Model Involving Three Different Fractional Operators,” Advances in Materials Science, vol. 23, issue (2), pp.25-44. DOI: 10.2478/adms-2023-0009 (Web of Science, Google Scholar) IF 1.8 - 2023 - в издания, индексирани в Scopus или Web of Science
23. Saddiqa, M., Ullah, S., Tawfiq, F.M., Ro, J.S., Farid, G. and Zainab, S., 2023. “k-Fractional inequalities associated with a generalized convexity,” AIMS Mathematics, vol. 8, issue (12), pp.28540-28557. ISSN 24736988, DOI 10.3934/math.20231460 (Web of Science, Scopus, Google Scholar) SJR 0.455, IF 2.2 - 2023 - в издания, индексирани в Scopus или Web of Science
24. Ali, K.K., Mohamed, M.S. and Maneea, M., 2023. “Exploring optical soliton solutions of the time fractional q-deformed Sinh-Gordon equation using a semi-analytic method,” AIMS Mathematics, vol. 8, issue (11), pp.27947-27968. ISSN 24736988, DOI 10.3934/math.20231429 (Web of Science, Scopus, Google Scholar) SJR 0.455, IF 2.2 - 2023 - в издания, индексирани в Scopus или Web of Science
25. Molla, M.A.K. and Mallik, S.H., 2023. “Time-nonlocal six-phase-lag generalized theory of thermoelastic diffusion,” Mechanics Based Design of Structures and Machines, vol. 51, issue (11), pp.6123-6141. ISSN 15397734, DOI 10.1080/15397734.2022.2036997 (Web of Science, Scopus, Google Scholar) SJR 0.646, IF 3.9 - 2023 - в издания, индексирани в Scopus или Web of Science
26. Sepasian, N., & Tavazoei, M. S. (2024). “Deviation analysis in transient response of fractional-order systems: An elementary function-based lower bound,” Journal of Vibration and Control, https://doi.org/10.1177/10775463241263, ISSN 1077-5463 (Web of Science, Google Scholar) IF 2.6 - 2024 - в издания, индексирани в Scopus или Web of Science
27. Liu, J., Ling, B. W. K., Zhou, Z., Wu, W., Li, R., & Liu, Q. (2024). “Classification of electroencephalograms before or after applying transcutaneous electrical nerve stimulation therapy using fractional empirical mode decomposition,” Multimedia Tools and Applications, pp. 1-24. https://doi.org/10.1007/s11042-024-19992-1 (Web of Science, Google Scholar) IF 3.0 - 2024 - в издания, индексирани в Scopus или Web of Science
28. Hassan, A. F., Abidou, D., Elsaid, A., & Zahra, W. K. (2024). “Fractional non-Fourier modeling of laser drilling process,” Physica Scripta, vol. 99, issue (8), ISSN 00318949, DOI 10.1088/1402-4896/ad5ed2 (Web of Science, Scopus, Google Scholar) IF 2.3, SJR 0.415 - 2024 - в издания, индексирани в Scopus или Web of Science
29. Doctolero, S., & Westwick, D. (2024, July). “Fractional-Order Integral Neural-Adaptive Control of Nonlinear Input-Affine Systems,” In 2024 American Control Conference (ACC) (pp. 4359-4364). IEEE. ISSN 07431619, ISBN 979-835038265-5, DOI 10.23919/ACC60939.2024.10644168 (Scopus, Google Scholar) - 2024 - в издания, индексирани в Scopus или Web of Science
30. Rabiei, F., Ali, Z., Hosseini, K., & Bhatti, M. M. (2024). “Optimal homotopy asymptotic method with Caputo fractional derivatives: a new approach for solving time-fractional Navier-Stokes equation,” In Nanofluids (pp. 277-312). Elsevier. ISBN 978-044313625-2, 978-044313626-9, DOI 10.1016/B978-0-443-13625-2.00009-7 (Scopus, Google Scholar) - 2024 - в издания, индексирани в Scopus или Web of Science
31. Marichev, O., & Shishkina, E. (2024). “Overview of fractional calculus and its computer implementation in Wolfram Mathematica,” Fractional Calculus and Applied Analysis, pp. 1-68. ISSN 13110454, DOI 10.1007/s13540-024-00332-x (Web of Science, Scopus, Google Scholar) IF 2.7, SJR 0.838 - 2024 - в издания, индексирани в Scopus или Web of Science
32. Devi, O. L., & Singh, A. 2024 “Performance analysis of fractional‐order modified SRF PLL under grid abnormalities,” International Journal of Circuit Theory and Applications. ISSN 00989886, DOI 10.1002/cta.4161 (Web of Science, Scopus, Google Scholar) IF 1.8, SJR 0.38 - 2024 - в издания, индексирани в Scopus или Web of Science
33. Hassan, A. F., Abidou, D., Elsaid, A., & Zahra, W. K. (2024). “Fractional non-Fourier modeling of laser drilling process,” Physica Scripta, vol. 99, issue (8), ISSN 00318949, DOI 10.1088/1402-4896/ad5ed2. (Web of Science, Scopus, Google Scholar) IF 2.6, SJR 0.415 - 2024 - в издания, индексирани в Scopus или Web of Science
34. Ali, K. K., Mohamed, M. S., Alharbi, W. G., & Maneea, M. (2024). “Solving the time fractional q-deformed tanh-Gordon equation: A theoretical analysis using controlled Picard’s transform method,” AIMS Mathematics, vol. 9, issue (9), pp. 24654-23676. ISSN 24736988, DOI 10.3934/math.20241201 (Scopus, Google Scholar) SJR 0.456 - 2024 - в издания, индексирани в Scopus или Web of Science
35. Fantini, V., & Fenyes, A. (2024). “The regularity of ODEs and thimble integrals with respect to Borel summation,” arXiv preprint arXiv:2407.01412. pp. 1-87, https://doi.org/10.48550/arXiv.2407.01412 (Google Scholar) - 2024 - в издания, индексирани в Scopus или Web of Science
36. Lazarević, M. P., Radojević, D. M., Pišl, S., & Živković, N. L. (2024, June). “Fractional order time delayed acceleration feedback control of inverted pendulum system,” In 2024 32nd Mediterranean Conference on Control and Automation (MED) (pp. 346-351). IEEE. ISBN 979-835039544-0, DOI 10.1109/MED61351.2024.10566149 (Scopus, Google Scholar) - 2024 - в издания, индексирани в Scopus или Web of Science
37. Molla, M. A. K., & Mallik, S. H. (2024). “Time-nonlocal six-phase-lag generalized theory of thermoelastic diffusion with two-temperature,” Waves in Random and Complex Media, vol. 34, issue (4), pp. 3281-3304. ISSN 17455030, DOI 10.1080/17455030.2021.1974601 (Web of Science, Scopus, Google Scholar) IF 4.051, SJR 0.483 - 2024 - в издания, индексирани в Scopus или Web of Science
38. TARTAGLIONE, V., 2024, DE L’UNIVERSITÉ DE BORDEAUX. (Google Scholar) - 2024 - от чужди автори в чужди издания, неиндексирани в Scopus или Web of Science
39. Hedrih, K.R.S. and Milovanović, G.V., 2024. „Elements of mathematical phenomenology and analogies of electrical and mechanical oscillators of the fractional type with finite number of degrees of freedom of oscillations: linear and nonlinear modes“ Communications in Analysis and Mechanics, vol. 16, issue (4), pp.738-785. doi: 10.3934/cam.2024033 (Web of Science, Scopus, Google Scholar) - 2024 - в издания, индексирани в Scopus или Web of Science
40. Ajmal, M., Rafaqat, M. and Ahmed, L., 2023. “Caputo Fractional Derivative Inequalities for modified (h, m)− Convex Functions,” Corros. Mater, vol. 48, pp.101-115. (Google Scholar) - 2024 - от чужди автори в чужди издания, неиндексирани в Scopus или Web of Science
41. Lazarević, M., Pišl, S., Radojević, D. and Nešić, N., 2024. “STABILITY OF FRACTIONAL-ORDER TIME-DELAY DYNAMICAL SYSTEMS: NEW RESULTS,” In Booklet of abstracts of the “2nd International Conference on Mathematical Modelling in Mechanics and Engineering”, Belgrade, 12.-14. September 2024. (pp. 91-92). Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade. (Google Scholar) - 2024 - от чужди автори в чужди издания, неиндексирани в Scopus или Web of Science
42. Benali, H., Souid, M.S., Günerhan, H. and Fernandez-Gamiz, U., 2024. “Estimates related to Caputo derivatives using generalized modified h-convex functions,” AIMS Mathematics, vol. 9, issue (10), pp.28813-28827. ISSN 24736988, DOI 10.3934/math.20241398 (Web of Science, Scopus, Google Scholar) IF 1.7, SJR 0.456 - 2024 - в издания, индексирани в Scopus или Web of Science
43. Ali, K.K., Maneea, M. and Mohamed, M.S., 2023. “Solving Nonlinear Fractional Models in Superconductivity Using the q‐Homotopy Analysis Transform Method,” Journal of Mathematics, vol. 2023, issue (1), pp. 1-23, ISSN 23144629, DOI 10.1155/2023/6647375 (Scopus, Google Scholar) IF 1.3, SJR 0.31 - 2024 - в издания, индексирани в Scopus или Web of Science
Вид: публикация в международен форум, публикация в реферирано издание, индексирана в Google Scholar
