Skip to main content
SpringerLink
Log in

Solution Strategy for Fuzzy Fractional Order Linear Homogeneous Differential Equation by Caputo-H Differentiability and Its Application in Fuzzy EOQ Model

  • Chapter
  • First Online:
Advances in Fuzzy Integral and Differential Equations

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 412))

Abstract

This chapter aims to describe a stock dependent memory concerned EOQ model in fuzzy uncertain situation. Before developing the EOQ model, a brief theory of fuzzy fractional linear homogeneous differential equation inspired by Caputo H differentiability has been established in this paper. In the fuzzy fractional linear homogeneous differential equation, both the co-efficient and the initial value are assumed to be fuzzy number.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Diethelm, K., Baleanu, D., Scalas, E.: Fractional Calculus: Models and Numerical Methods. World Scientific (2012)

    Google Scholar 

  2. Mainardi, F.: Fractional Calculus, Fractals and Fractional Calculus in Continuum Mechanics (1997)

    Google Scholar 

  3. Agila, A., Baleanu, D., Eid, R., Iranfoglu, B.: Applications of the extended fractional Euler-Lagrange equations model to freely oscillating dynamical systems. Rom. J. Phys. 61, 350–359 (2016)

    Google Scholar 

  4. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego, CA (1999)

    MATH  Google Scholar 

  5. Agarwal, R.P., Lakshmikantham, V., Nieto, JJ.: On the concept of solutions for fractional differential equations with uncertainty. Non Linear Annal. 72, 2859–2862 (2010)

    Google Scholar 

  6. Hoa, N.V., Lupulescu, V., Regan, D.O.: A note on initial value problems for fractional fuzzy differential equations. Fuzzy Sets Syst. (2017). https://doi.org/10.1016/j.fss.2017.10.002

    Article  Google Scholar 

  7. Lupulescu, V., Hoa, N.V., Regan, D.O.: Solving interval valued fractional initial value problems under Caputo gH- fractional differentiability. Fuzzy Sets Syst. (2016). https://doi.org/10.1016/j.fss.2016.09.015

    Article  Google Scholar 

  8. Allahviranloo, T., Ahmadi, M.B.: Fuzzy Laplace transforms. Soft. Comput. 14, 235–243 (2010). https://doi.org/10.1007/s00500-008-0397-6

    Article  MATH  Google Scholar 

  9. Salahshour, S., Allahviranloo, T.: Applications of fuzzy Laplace transforms. Soft. Comput. 17, 145–158 (2013). https://doi.org/10.1007/s00500-012-0907-4

    Article  MATH  Google Scholar 

  10. Salahshour, S., Allahviranloo, T., Abbasbandy, S.: Solving fuzzy fractional differential equations by fuzzy Laplace transforms. Commun Nonlinear Sci. Numer. Simulat. 17, 1372–1381 (2012)

    Article  MathSciNet  Google Scholar 

  11. Allahviranloo, T., Salahshour, S., Abbasbandy, S.: Explicit solutions of fractional differential equations with uncertainty. Soft Comput. https://doi.org/10.1007/s00500-011-0743-y

  12. Mazandrarami, M., VahidianKamyad, A.: Modified fractional Euler method for solving fuzzy fractional initial value problem. Commun. Nonlinear Sci. Numer. Simul. 18, 12–21 (2013)

    Article  MathSciNet  Google Scholar 

  13. Salahshour, S., Allahviranloo, T., Abbasbandy, S., Baleanu, D.: Existence and uniqueness results for fractional differential equations with uncertainty. Adv. Diff. Equ. 112 (2012). https://doi.org/10.1186/1687-1847-2012-112

  14. Salahshour, S., Ahmadian, A., Senu, N., Baleanu, D., Agarwal, P.: On analytical solutions of the fractional differential equations with uncertainty: application to the Basset problem. Entropy 17, 885–902 (2015). https://doi.org/10.3390/e17020885

    Article  MathSciNet  MATH  Google Scholar 

  15. Pakhira, R., Ghosh, U., Sarkar, S.: Application of memory effects in an inventory model with price dependent demand rate during shortage. Int. J. Educ. Manage. Eng. 3, 51–64 (2019)

    Article  Google Scholar 

  16. Rahaman, M., Mondal, S.P., Shaikh, A.A., et al.: Arbitrary-order economic production quantity model with and without deterioration: generalized point of view. Adv. Differ. Equ. 2020, 16 (2020). https://doi.org/10.1186/s13662-019-2465-x

    Article  MathSciNet  Google Scholar 

  17. Rahaman, M., Mondal, S.P., Shaikh, A.A., et al.: Artificial bee colony optimization-inspired synergetic study of fractional-order economic production quantity model. Soft. Comput. (2020). https://doi.org/10.1007/s00500-020-04867-y

    Article  Google Scholar 

  18. Chakraborty, A., Maity, S., Jain, S., Mondal, SP., Alam, S.: Hexagonal fuzzy number and its distinctive representation, ranking, defuzzification technique and application in production inventory management problem. Granular Comput. 1–15 (2020)

    Google Scholar 

  19. Chakraborty, A., Mondal, S.P., Alam, S., Ahmadian, A., Senu, N., De, D., Salahshour, S.: The pentagonal fuzzy number: its different representations, properties, ranking, defuzzification and application in game problems. Symmetry 11(2), 248 (2019)

    Article  Google Scholar 

  20. Mondal, S.P., Mandal, M.: Pentagonal fuzzy number, its properties and application in fuzzy equation. Future Comput. Inf. J. 2(2), 110–117 (2017)

    Article  Google Scholar 

  21. Mondal, S.P.: Differential equation with interval valued fuzzy number and its applications. Int. J. Syst. Assurance Eng. Manage. 7(3), 370–386 (2016)

    Article  Google Scholar 

  22. Allahviranloo, T., Abbasbandy, S., Sedaghgatfar, O., Darabi, P.: A new method for solving fuzzy integro-differential equation under generalized differentiability. Neural Comput. Appl. 21, 191–196 (2012)

    Article  Google Scholar 

  23. Hajighasemi, S., Allahviranloo. T., Khezerloo, M., Khorasany M., Salahshour S.: Existence and uniqueness of solutions of fuzzy volterra integro-differential equations. In: Communications in Computer and Information Science, Vol. 81, Part 2, 2010, pp. 491–500, 13th International Conference on Information Processing and Management of Uncertainty, IPMU 2010, Dortmund, Germany, 28 June 2010 through 2 July 2010, Code 98056 (Conference Paper)

    Google Scholar 

  24. Gouyandeh, Z., Allahviranloo, T., Abbasbandy, S.: A fuzzy solution of heat equation under generalized Hukuhara differentiability by fuzzy Fourier transform. Fuzzy Sets Syst. 309(15), 81–97 (2017)

    Article  MathSciNet  Google Scholar 

  25. Allahviranloo, T., Abbasbandy, S., Rouhparvar, H.: The exact solutions of fuzzy wave-like equations with variable coefficients by a variational iteration method. Appl. Soft Comput. J. 11(2), 2186–2192 (2011)

    Article  Google Scholar 

  26. Chehlabi, M., Allahviranloo, T.: Concreted solutions to fuzzy linear fractional differential equations. Appl. Soft Comput. J. 44, 108–116 (2016)

    Article  Google Scholar 

  27. Allahviranloo, T., Lotfi, F.H., Kiasari, M.K., Khezerloo, M.: On the fuzzy solution of LR fuzzy linear systems. Appl. Math. Model. 37(3), 1170–1176 (2013)

    Article  MathSciNet  Google Scholar 

  28. Allahviranloo, T., Amirteimoori, A., Khezerloo, M., Khezerloo, S.: A new method for solving fuzzy Volterra integro-differential equations. Aust. J. Basic Appl. Sci. 5(4), 154–164 (2011)

    MATH  Google Scholar 

  29. Allahviranloo, T., Salahshour, S.: Fuzzy symmetric solutions of fuzzy linear systems. J. Comput. Appl. Math. 235(16), 4545–4553 (2011)

    Article  MathSciNet  Google Scholar 

  30. Allahviranloo, T., Salahshour, S., Khezerloo, M.: Maximal- and minimal symmetric solutions of fully fuzzy linear systems. J. Comput. Appl. Math. 235(16), 4652–4662 (2011)

    Article  MathSciNet  Google Scholar 

  31. Allahviranloo, T., Ahmady, E., Ahmady, N.: Nth-order fuzzy linear differential equations. Inf. Sci. 178(5), 1309–1324 (2008)

    Article  Google Scholar 

  32. Allahviranloo, T., Abbasbandy, S., Ahmad, N., Ahmady, E.: Improved predictor-corrector method for solving fuzzy initial value problems. Inf. Sci. 179(7), 945–955 (2009)

    Article  MathSciNet  Google Scholar 

  33. Abbasbandy, S., Allahviranloo, T.: Method applied to the Fuzzy system of Fredholm integral equations of the second kind. Int. J. Uncertain. Fuzz. Knowl. Based Syst. 14(1), 101–110 (2006)

    Article  MathSciNet  Google Scholar 

  34. Salahshour, S., Ahmadian, A., Ismail, F., Baleanu, D., Senu, N.: A new fractional derivative for differential equation of fractional order under interval uncertainty. Adv. Mech. Eng. 7(12), 1–11 (2015)

    Article  Google Scholar 

  35. Ahmadian, A., Chan, S., Salahshour, S., Vaitheeswaran V.: FTFBE: a numerical approximation for fuzzy time-fractional Bloch equation. In: IEEE International Conference on Fuzzy Systems, 4 September 2014, Article number 6891696, pp 418–423, 2014 IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2014, Beijing, China, 6 July 2014 through 11 July 2014, Category number CFP14FUZ-ART, Code 114802

    Google Scholar 

  36. Salahshour, S., Ahmadian, A., Ismail, F., Baleanu, D.: A fractional derivative with non-singular kernel for interval-valued functions under uncertainty. Optik 130(1), 273–286 (2017)

    Article  Google Scholar 

  37. Ahmadian, A., Salahshour, S., Ali-Akbari, M., Ismail, F., Baleanu, D.: A novel approach to approximate fractional derivative with uncertain conditions. Chaos, Solitons Fractals 104, 68–76 (2017)

    Article  MathSciNet  Google Scholar 

  38. Salahshour, S., Ahmadian, A., Chan, C.S.: Successive approximation method for Caputo q-fractional IVPs. Commun. Nonlinear Sci. Numer. Simul. 24(1–3), 153–158 (2015)

    Article  MathSciNet  Google Scholar 

  39. Rabiei, F., Ismail, F., Ahmadian, A., Salahshour S.: Numerical solution of second-order fuzzy differential equation using improved Runge-kutta nystrom method. Math. Prob. Eng., Article number 803462 (2013)

    Google Scholar 

  40. Shahriyar, M.R.B, Ismail, F., Aghabeigi, S., Ahmadian, A., Salahshour, S.: An eigenvalue-eigenvector method for solving a system of fractional differential equations with uncertainty. Math. Prob. Eng., Article number 579761 (2013)

    Google Scholar 

  41. Allahviranloo, T., Khezerloo, M., Sedaghatfar, O., Salahshour, S.: Toward the existence and uniqueness of solutions of second-order fuzzy Volterra integro-differential equations with fuzzy kernel. Neural Comput. Appl. 22(SUPPL 1), 133–141 (2013)

    Google Scholar 

  42. Allahviranloo, T., Salahshour, S.: A new approach for solving first order fuzzy differential equation. In: Communications in Computer and Information Science, vol. 81, Part 2, 2010, pp. 522–531, 13th International Conference on Information Processing and Management of Uncertainty, IPMU 2010, Dortmund, Germany, 28 June 2010 through 2 July 2010, Code 98056

    Google Scholar 

  43. Salahshour, S., Ahmadian, A., Senu, N., Baleanu, D., Agarwal, P.: On analytical solutions of the fractional differential equation with uncertainty: application to the basset problem. Entropy 17(2), 885–902 (2015)

    Article  MathSciNet  Google Scholar 

  44. Allahviranloo, T., Abbasbandy, S., Salahshour, S., Hakimzadeh, A.: A new method for solving fuzzy linear differential equations. Computing (Vienna/New York) 92(2), 181–197 (2011)

    Google Scholar 

  45. Salahshour, S., Ahmadian, A., Pansera, B., Ferrara, M.: Uncertain inverse problem for fractional dynamical systems using perturbed collage theorem. Commun. Nonlin. Sci. Numer. Simul. 94, Article number 105553 (2021)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, India

    Mostafijur Rahaman & Shariful Alam

  2. Department of Applied Science, Maulana Abul Kalam Azad University of Technology, West Bengal, Kolkata, India

    Sankar Prasad Mondal

  3. LMACS, Laboratoire de Mathematiques Appliquees & Calcul Scientique, Sultan Moulay Slimane University, PO Box 523, 23000, Beni Mellal, Morocco

    A. El Allaoui

  4. Institute of IR 4.0, The National University of Malaysia, UKM, 43600, Bangi, Selangor, Malaysia

    Ali Ahmadian

  5. Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey

    Soheil Salahshour

Authors
  1. Mostafijur Rahaman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sankar Prasad Mondal
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. El Allaoui
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shariful Alam
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ali Ahmadian
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Soheil Salahshour
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculty of Engineering and Natural Sciences, Bahçeşehir University, Istanbul, Turkey

    Tofigh Allahviranloo

  2. Faculty of Engineering and Natural Sciences, Bahçeşehir University, Istanbul, Turkey

    Soheil Salahshour

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Rahaman, M., Mondal, S.P., El Allaoui, A., Alam, S., Ahmadian, A., Salahshour, S. (2022). Solution Strategy for Fuzzy Fractional Order Linear Homogeneous Differential Equation by Caputo-H Differentiability and Its Application in Fuzzy EOQ Model. In: Allahviranloo, T., Salahshour, S. (eds) Advances in Fuzzy Integral and Differential Equations. Studies in Fuzziness and Soft Computing, vol 412. Springer, Cham. https://doi.org/10.1007/978-3-030-73711-5_5

Download citation

Publish with us

Policies and ethics

Search

Navigation