The Conformable Derivative Is Used to Solve a Fractional Differential Equation Analytically

Salim Saeed Mahmood; Sarwar Ahmad Hamad; Kamaran Jamal Hamad; Aso Kurdo Ahmed

doi:10.25212/lfu.qzj.7.1.44

توێژەران

Salim Saeed Mahmood Department of Mathematic, Faculty of Science, Soran University, Kurdistan Regional Government, Iraq
Sarwar Ahmad Hamad Department of Mathematic, Faculty of Science, Zakho University, Kurdistan Regional Government, Iraq.
Kamaran Jamal Hamad Department of Mathematic, Faculty of Science, Soran University, Kurdistan Regional Government, Iraq.
Aso Kurdo Ahmed Department of Business Administration, College of Administration and Economics, Lebanese French University, Kurdistan Region, Iraq

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https://doi.org/10.25212/lfu.qzj.7.1.44

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Fractional derivative, fractional integral, Conformable derivative Euler's equation

پوختە

In this paper, we talk about Fractional differential equations are generalizations of ordinary differential equations to an arbitrary (non-integer) order. Fractional differential equations have attracted considerable interest because of their ability to model complex phenomena. These equations capture nonlocal relations in space and time with power-law memory kernels. Due to the extensive applications of FDEs in engineering and science, research in this area has grown significantly all around the world.

Almost the arrangement representation of fragmentary differential equation with distinctive conditions and deals with some methods for analytically solving the linear and non-linear of fractional differential equation based upon a conformable derivative by several methods and illustrate many example.

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سەرچاوەکان

A. A. H. M. S. a. J. J. T. Kilbas, „. ,. (2006). Theory and applications of fractional differential equations. elsevier,, Vol. 204.

Abdulsamad, T., Kakarash, Z. A., Othman, R., Omar, S., & Ahmed, N. (2022). Distributed Resource Allocation Model with Presence of Multiple Jammer for Underwater Wireless Sensor Networks. Iraqi Journal For Computer Science and Mathematics, 3(1).

Ahmed, N. F., Omar, S. A., Othman, R. N., & Kakarash, Z. A. (2021). SQL Processor based on Intelligence Technique: Fuzzy Petri Net Database Applications. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 12(14), 1364-1371.

Al-Tarawneh, S. A. (2016). Solving Fractional Differential Equations by Using Conformable Fractional Derivatives Definition. Zarqa University, Jordan.

Bali, N. P. (2005). Golden real analysis. Firewall Media.

D. Y. Abdulwahab, „. ,. (2019). Properties and Application of the Caputo Fractional Operator. Baghdad: Baghdad University.

Guzman, .. M. (2018. ). A new definition of a fractional derivative of local type. Journal of Mathematical Analysis, pp. 88-98.

Hammad, M. A. ( 2014). Abel's formula and wronskian for conformable fractional differential equations. International Journal of Differential Equations and Applications, p. 13.3,.

Haubold, H. J. (2011). Mittag-Leffler functions and their applications. Journal of Applied Mathematics.

Horani, M. A. ( 2016). Variation of parameters for local fractional nonhomogenous linear differential equations. J. Math. Comput. Sci , pp. 147-153.

Ishteva, M. (2005). Properties and applications of the Caputo fractional operator,. University of Karlsruhe.

Iyiola, O. S. (2016). Some new results on the new conformable fractional calculus with application using D’Alambert approach,. Progr. Fract. Differ. Appl,, pp. 115-122.

J. L. Schiff, T. ( 2013). he Laplace transform: theory and applications. Business Media.

Jamil, D. I., Saleh, D. M., & Rahim, A. G. (2018). Construction of New Standardized Attribute Control Chart based on defects per million opportunities. QALAAI ZANIST SCIENTIFIC JOURNAL, 3(3), 734-745.

Kareem, A. M. ( 2017). Conformable fractional derivatives and it is applications for solving fractional differential equations. J. Math, pp. 81-87.

Kh, T. I., & Hamarash, I. I. (2021). MODEL-Based Performance Quality Assessment for IoT Applications. iJIM, 15(12), 5.

Khalil, R. e. (2014). A new definition of fractional derivative. Journal of Computational and Applied Mathematics, pp. 65-70.

Khalil, R. M. (2016). Undetermined coefficients for local fractional differential equations. J. Math. Comput, pp. 140-146.

Kadir, D. H., Saleh, D. M., & Jamil, D. I. Comparison between four Methods to Construction Number of Defectives Control Chart.

Kimeu, J. M. (2009). Fractional calculus: Definitions and applications.

Koning, D. E. (2015). Fractional Calculus. Diss.

M. J. B. a. Z. A. Ilie. (2018). General solution of second order fractional differential equations. Int. J. Appl. Math., pp. 56-61.

Matlob, M. a. (2017). he Concepts and Applications of Fractional Order Differential Calculus in Modelling of Viscoelastic Systems,.

Matlob, M. A. (2019). „The concepts and applications of fractional order differential calculus in modeling of viscoelastic systems. Critical Reviews.

Milici, C. G. (2019). Introduction to fractional differential equations. Springer.

Oliveira, .. C. (2014.). A review of definitions for fractional derivatives and integral,. Mathematical Problems in Engineering.

Oliveira, E. C. (2019). Solved Exercises in Fractional Calculus. Springer International Publishing.

Omar, A. A. (2017). The Numerical Solution of Linear Variable Order Fractional Differential Equations Using Bernstein Polynomials.

Ortigueira, M. D. (2015). What is a fractional derivative? Journal of computational Physics, pp. 4-13,.

Ouyang, Y. a. (2016). Comparison of Definition of Several Fractional Derivatives,. International Conference on Education.

Podlubny, I. (1998.). Fractional differential equations: an introduction to fractional derivatives. Elsevier.

Saleh, D. M., & Jamil, D. I. (2017). Construction Three Charts Based on Inter Quartile Range and Comparison of Efficiency with Three Charts Based on Range. Qalaai Zanist Scientific Journal, 2(3), 317-329.

Sene, N. (2018). Solutions for some conformable differential equations. Progr. Fract. Differ Appl , pp. 493-501.

T.Abdeljawad. (pp. 57-66). On conformable fractional calculus. Journal of computational and Applied Mathematics,, 2015.

Z. H. O. U. W. J. a. Z. L. Yong. (2016). Basic theory of fractional differential equations. World Scientific,.