Application of Laplace transform to solve fractional integro-differential equations

Volume 33, Issue 3, pp 225--237 https://dx.doi.org/10.22436/jmcs.033.03.02

Publication Date: January 13, 2024 Submission Date: August 29, 2023 Revision Date: September 21, 2023 Accteptance Date: October 14, 2023

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 196 Downloads
• 1282 Views

Authors

Gunasekar Gunasekar - Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R\(\&\)D Institute of Science and Technology, Chennai-600062, Tamil Nadu, India. P. Raghavendran - Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R\(\&\)D Institute of Science and Technology, Chennai-600062, Tamil Nadu, India. Sh. S. Santra - Department of Mathematics, JIS College of Engineering, Kalyani, West Bengal 741235, India. D. Majumder - Department of Mathematics, JIS College of Engineering, Kalyani-741235, West Bengal 741235, India. D. Baleanu - Institute of Space Sciences, Magurele-Bucharest, 077125 Magurele, Romania. H. Balasundaram - Department of Mathematics, Rajalakshmi Institute of Technology, Chennai-600124, Tamil Nadu, India.

Abstract

This paper reveals the solutions to several families of fractional integro-differential equations through the application of a simple fractional calculus method. This approach results in various interesting consequences and also extends the classical Frobenius method. The provided approach is primarily based on established theorems concerning particular solutions of fractional integro-differential equations using the Laplace transform and the extension coefficients of binomial series. Additionally, an illustrative example of such fractional integro-differential equations is presented.

Share and Cite

Keywords

• Riemann-Liouville fractional integrals
• fractional-order differential equation
• gamma function
• Mittag-Leffler function
• Wright function
• Laplace transform of the fractional derivative

MSC

•  26A33
•  44A10
•  34A05
•  33D05
•  33E12

References

• [1] M. Bohner, T. Li, Kamenev-type criteria for nonlinear damped dynamic equations, Sci. China Math., 58 (2015), 1445–1452
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [2] M. Caputo, Elasticit`a e Dissipazione, Zanichelli, Bologna (1969)
  • View Article


• [3] A. Columbu, S. Frassu, G. Viglialoro, Properties of given and detected unbounded solutions to a class of chemotaxis models, Stud. Appl. Math., 151 (2023), 1–31
  • View Article
  • MathSciNet
  • Google Scholar


• [4] J. Dˇzurina, S. R. Grace, I. Jadlovsk´a, T. Li, Oscillation criteria for second-order Emden-Fowler delay differential equations with a sublinear neutral term, Math. Nachr., 293 (2020), 910–922
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [5] T. M. Elzaki, S. M. Elzaki, T. M. Elzaki, S. M. Elzaki, Elixir Appl. Math., 36 (2011), 3226–3229
  • View Article
  • Google Scholar


• [6] R. Gorenflo, S. Vessella, Abel integral equations: Analysis and applications, Lecture Notes in Mathematics, Springer- Verlag, , Berlin (1991)
  • View Article
  • Google Scholar


• [7] C. Jayakumar, S. S. Santra, D. Baleanu, R. Edwan, V. Govindan, A. Murugesan, M. Altanji, Oscillation result for Half-Linear delay difference equations of second order, Math. Biosci. Eng., 19 (2022), 3879–3891
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] B. Jin, Fractional differential equations—an approach via fractional derivatives, Springer, Cham (2021)
  • View Article
  • MathSciNet
  • Google Scholar


• [9] K. Karthikeyan, A. Debbouche, D. F. M. Torres, Analysis of Hilfer fractional integro-differential equations with almost sectorial operators, Fractal Fract., 5 (2021), 1–13
  • View Article
  • Google Scholar


• [10] V. Kiryakova, Commentary: A remark on the fractional integral operators and the image formulas of generalized Lommel- Wright function, Front. Phys., 7 (2019), 4 pages
  • View Article
  • Google Scholar


• [11] V. Lakshmikantham, M. Rama Mohana Rao, Theory of integro-differential equations, Gordon and Breach Science Publishers, Lausanne (1995)
  • View Article
  • Google Scholar


• [12] V. Lakshmikantham, A. S. Vatsala, Basic theory of fractional differential equations, Nonlinear Anal., 69 (2008), 2677– 2682
  • View Article
  • MathSciNet
  • Google Scholar


• [13] T. Li, S. Frassu, G. Viglialoro, Combining effects ensuring boundedness in an attraction-repulsion chemotaxis model with production and consumption, Z. Angew. Math. Phys., 74 (2023), 21 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [14] T. Li, N. Pintus, G. Viglialoro, Properties of solutions to porous medium problems with different sources and boundary conditions, Z. Angew. Math. Phys., 70 (2019), 18 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [15] T. Li, Y. V. Rogovchenko, On asymptotic behavior of solutions to higher-order sublinear Emden-Fowler delay differential equations, Appl. Math. Lett., 67 (2017), 53–59
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [16] T. Li, Y. V. Rogovchenko, On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations, Appl. Math. Lett., 105 (2020), 7 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [17] T. Li, G. Viglialoro, Boundedness for a nonlocal reaction chemotaxis model even in the attraction-dominated regime, Differential Integral Equations, 34 (2021), 315–336
  • View Article
  • Google Scholar
  • MATH


• [18] S.-D. Lin, C.-H. Lu, Laplace transform for solving some families of fractional differential equations and its applications, Adv. Difference Equ., 2013 (2013), 9 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [19] F. Masood, O. Moaaz, S. S. Santra, U. Fernandez-Gamiz, H. A. El-Metwally, Oscillation theorems for fourth-order quasi-linear delay differential equations, AIMS Math., 8 (2023), 16291–16307
  • View Article
  • MathSciNet
  • Google Scholar


• [20] G. M. Mittag-Leffler, Sur la nouvelle fonction E(x), C. R. Acad. Sci. Paris, 137 (1903), 554–558
  • View Article
  • Google Scholar


• [21] C. Muthamilarasi, S. S. Santra, G. Balasubramanian, V. Govindan, R. A. El-Nabulsi, K. M. Khedher, The stability analysis of A-Quartic functional equation, Mathematics, 9 (2021), 16 pages
  • View Article
  • Google Scholar


• [22] D. Patil, Dualities between double integral transforms, Int. Adv. J. Sci., Eng. Technol., 7 (2020), 57–64
  • View Article
  • Google Scholar


• [23] D. Patil, Application of integral transform (Laplace and Shehu) in chemical sciences, Aayushi Int. Interdiscip. Res. J., (2022), 437–441
  • View Article
  • Google Scholar


• [24] R. Saadeh, A generalized approach of triple integral transforms and applications, J. Math., 2023 (2023), 12 pages
  • View Article
  • MathSciNet
  • Google Scholar


• [25] S. S. Santra, P. Mondal, M. E. Samei, H. Alotaibi, M. Altanji, T. Botmart, Study on the oscillation of solution to second-order impulsive systems, AIMS Math., 8 (2023), 22237–22255
  • View Article
  • MathSciNet
  • Google Scholar


• [26] F. S. Silva, D. M. Moreira, M. A. Moret, Conformable Laplace transform of fractional differential equations, Axioms, 7 (2018), 1–12
  • View Article
  • Google Scholar


• [27] H. M. Srivastava, 1 An Introductory Overview of Special Functions and Their Associated Operators of Fractional Calculus, Special Functions Fract. Calc. Eng., (2023), 1–35
  • View Article
  • Google Scholar


• [28] N. E. H. Taha1, R. I. Nuruddeen, A. K. H. Sedeeg, Dualities between”Kamal & Mahgoub Integral Transforms”and”Some Famous Integral Transforms”, Br. J. Appl. Sci. Technol., 20 (2017), 1–8
  • View Article
  • Google Scholar


• [29] A. Y¨ uce, N. Tan, Inverse Laplace transforms of the fractional order transfer functions, In: 2019 11th International Conference on Electrical and Electronics Engineering (ELECO), IEEE., (2019), 775–779
  • View Article
  • Google Scholar