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Year 2024, Volume: 42 Issue: 2, 313 - 320, 30.04.2024

Norravich Limpanukorn Idris Ahmed Muhammad Jamilu Ibrahim

Abstract

References

  • REFERENCES
  • [1] Ahmed I, Baba IA, Yusuf A, Kumam P, Kumam W. Analysis of Caputo fractional-order model for COVID-19 with lockdown. Adv Differ Equ 2020;2020:394.
  • [2] Ahmed I, Gouf EFD, Yusuf A, Kumam P, Chaipanya P, Nonlaopon K. An epidemic prediction from analysis of a combined hiv-covid-19 co-infection model via ABC-fractional operator. Alex Eng J 2021;60:29792995.
  • [3] Alkhudhari Z, Sheikh S, Al-Tuwairqi S. Global dynamics of a mathematical model on smoking. Int Sch Res Not Appl Math 2014;2014:847075.
  • [4] Alzahrani E, Zeb A. Stability analysis and prevention strategies of tobacco smoking model. Bound Value Probl 2020;2020:3.
  • [5] Annaby MH, Mansour ZS. q-Fractional Calculus and Equations. Lecture Notes in Mathematics, vol 2056. Springer; 2012.
  • [6] Arif M, Kumam P, Kumam W, Akgul A, Sutthibutpong T. Analysis of newly developed fractal-fractional derivative with power law kernel for MHD couple stress fluid in channel embedded in a porous medium. Sci Rep 2021;11:20858.
  • [7] Atangana A. Extension of rate of change concept: From local to non-local operators with applications. Results Phys 2020;19.
  • [8] Belgaid Y, Helal M, Lakmeche A, Venturino E. A Mathematical Study of a Coronavirus Model with the Caputo Fractional-Order Derivative. Fractal Fract 2021;5:87.
  • [9] Bonyah E, Sagoe AK, Kumar D, Deniz S. Fractional optimal control dynamics of coronavirus model with Mittag-Leffler law. Ecol Complex 2021;45:100880.
  • [10] Borisut P, Khammahawong K, Kumam P. Fixed Point Theory Approach to Existence of Solutions with Differential Equations. IntechOpen; 2018.
  • [11] Burton TA. A Fixed-point theorem of Krasnoselskii. Appl Math Lett 1998;11:8588.
  • [12] Imran MA. Application of fractal fractional derivative of power law kernel to MHD viscous fluid flow between two plates. Chaos Solitons Fractals. 2020;134.
  • [13] Jackson FH. On q-functions and a certain difference operator. Trans R Soc Edinb 1909;46:253281.
  • [14] Jarad F, Abdeljawad T. Generalized fractional derivatives and Laplace transform. Discret Contin Dyn S 2020;13:709722.
  • [15] Kilbas A, Srivastava H, Trujillo J. Theory and Application of Fractional Differential Equation. North-Holland Mathematical Studies. Elsevier Science; 2006. pp. 69133.
  • [16] Limpanukorn N, Ahmed I, Ibrahim MJ. Uniqueness of continuous solution to q-Hilfer fractional hybrid integro-difference equation of variable order. J Math Anal Model 2021;2:8898.
  • [17] Limpanukorn N, Ngiamsunthorn PS. Existence and Ulam stability of solution to fractional order hybrid differential equation of variable order. Thai J Math 2020;18:453463.
  • [18] Meral FC, Royston TJ, Magin R. Fractional calculus in viscoelasticity: an experimental study. Commun Nonlinear Sci Numer Simul 2010;15:939945.
  • [19] Peng G. Some Monotonicity Properties of Gamma and q-Gamma Functions. Int Sch Res Notices 2011;2011:375715.
  • [20] Peter OJ. Transmission Dynamics of Fractional Order Brucellosis Model Using CaputoFabrizio Operator. Int J Differ Equ 2020;2020:2791380.
  • [21] Peter OJ, Shaikh AS, Ibrahim MO, Nisar KS, Baleanu D, Khan I, Abioye AI. Analysis and dynamics of fractional order mathematical model of COVID-19 in Nigeria using Atangana-Baleanu operator. Comput Mater Continua. 2021;66:18231848.
  • [22] Peter OJ, Yusuf A, Oshinubi K, Oguntolu PA, Ibrahim AA, Abioye AI, Ayoola TA. Fractional order of pneumococcal pneumonia ınfection model with caputo fabrizio operator. Results Phys 2021;29: 104581.
  • [23] Somjaiwang D, Ngiamsunthorn PS. Existence and approximation of solutions to fractional order hybrid differential equations. Adv Differ Equ 2016;2016:278.
  • [24] Tariboon J, Ntouyas SK, Agarwal P. New concepts of fractional quantum calculus and applications to impulsive fractional q-difference equations. Adv Differ Equ 2015;2015:18.
  • [25] Ahmed I, Kumam P, Jarad F, Jirakitpuwapat W. On Hilfer generalized proportional fractional derivative. Adv Differ Equ. 2020;2020:329.
  • [26] Ahmed I, Kumam P, Abubakar J, Borisut P, Sitthithakerngkiet K. Solutions for impulsive fractional pantograph differential equation via generalized anti- periodic boundary condition. Adv Differ Equ 2020;2020:1-15.
  • [27] Borisut P, Kumam P, Ahmed I, Sitthithakerngkiet K. Positive solution for nonlinear fractional differential equation with non-local multi-point condition. Fixed Point Theory 2020;21(2):427-440.
  • [28] Ahmed I, Yusuf A, Sani MA, Jarad F, Kumam W, Thounthong P. Analysis of a Caputo Hiv and Malaria co-infection Epidemic Model. Thai J Math 2021;19:897- 912.
  • [29] Mallah I, Ahmed I, Akgul A, Jarad F, Alha S. On ψ-Hilfer generalized proportional fractional operators. AIMS Mathematics. 2021;7:82-103.
  • [30] Borisut P, Kumam P, Ahmed I, Jirakitpuwapat W. Existence and uniqueness for ψ-Hilfer fractional differential equation with non-local multipoint condition. Math Methods Appl Sci. 2021;44:2506-2520.

On ψ-quantum fractional operators: Existence, uniqueness and Ulam-Hyers stability

Year 2024, Volume: 42 Issue: 2, 313 - 320, 30.04.2024

Norravich Limpanukorn Idris Ahmed Muhammad Jamilu Ibrahim

Abstract

In this paper, we study the generalized concept of q-calculus with respect to another func-tion. The 𝜓-quantum Riemann-Liouville fractional integral, 𝜓-quantum Riemann-Liouville fractional derivative, and 𝜓-quantum Caputo fractional derivative were introduced. The ex-istence, uniqueness, and Ulam-Hyers stability of the solutions with the mentioned derivatives were established. Finally, some examples are considered to demonstrate the results obtained.

Keywords

Q-Calculus ψ-Quantum Ulam-Hyers Stability Banach Contraction

References

  • REFERENCES
  • [1] Ahmed I, Baba IA, Yusuf A, Kumam P, Kumam W. Analysis of Caputo fractional-order model for COVID-19 with lockdown. Adv Differ Equ 2020;2020:394.
  • [2] Ahmed I, Gouf EFD, Yusuf A, Kumam P, Chaipanya P, Nonlaopon K. An epidemic prediction from analysis of a combined hiv-covid-19 co-infection model via ABC-fractional operator. Alex Eng J 2021;60:29792995.
  • [3] Alkhudhari Z, Sheikh S, Al-Tuwairqi S. Global dynamics of a mathematical model on smoking. Int Sch Res Not Appl Math 2014;2014:847075.
  • [4] Alzahrani E, Zeb A. Stability analysis and prevention strategies of tobacco smoking model. Bound Value Probl 2020;2020:3.
  • [5] Annaby MH, Mansour ZS. q-Fractional Calculus and Equations. Lecture Notes in Mathematics, vol 2056. Springer; 2012.
  • [6] Arif M, Kumam P, Kumam W, Akgul A, Sutthibutpong T. Analysis of newly developed fractal-fractional derivative with power law kernel for MHD couple stress fluid in channel embedded in a porous medium. Sci Rep 2021;11:20858.
  • [7] Atangana A. Extension of rate of change concept: From local to non-local operators with applications. Results Phys 2020;19.
  • [8] Belgaid Y, Helal M, Lakmeche A, Venturino E. A Mathematical Study of a Coronavirus Model with the Caputo Fractional-Order Derivative. Fractal Fract 2021;5:87.
  • [9] Bonyah E, Sagoe AK, Kumar D, Deniz S. Fractional optimal control dynamics of coronavirus model with Mittag-Leffler law. Ecol Complex 2021;45:100880.
  • [10] Borisut P, Khammahawong K, Kumam P. Fixed Point Theory Approach to Existence of Solutions with Differential Equations. IntechOpen; 2018.
  • [11] Burton TA. A Fixed-point theorem of Krasnoselskii. Appl Math Lett 1998;11:8588.
  • [12] Imran MA. Application of fractal fractional derivative of power law kernel to MHD viscous fluid flow between two plates. Chaos Solitons Fractals. 2020;134.
  • [13] Jackson FH. On q-functions and a certain difference operator. Trans R Soc Edinb 1909;46:253281.
  • [14] Jarad F, Abdeljawad T. Generalized fractional derivatives and Laplace transform. Discret Contin Dyn S 2020;13:709722.
  • [15] Kilbas A, Srivastava H, Trujillo J. Theory and Application of Fractional Differential Equation. North-Holland Mathematical Studies. Elsevier Science; 2006. pp. 69133.
  • [16] Limpanukorn N, Ahmed I, Ibrahim MJ. Uniqueness of continuous solution to q-Hilfer fractional hybrid integro-difference equation of variable order. J Math Anal Model 2021;2:8898.
  • [17] Limpanukorn N, Ngiamsunthorn PS. Existence and Ulam stability of solution to fractional order hybrid differential equation of variable order. Thai J Math 2020;18:453463.
  • [18] Meral FC, Royston TJ, Magin R. Fractional calculus in viscoelasticity: an experimental study. Commun Nonlinear Sci Numer Simul 2010;15:939945.
  • [19] Peng G. Some Monotonicity Properties of Gamma and q-Gamma Functions. Int Sch Res Notices 2011;2011:375715.
  • [20] Peter OJ. Transmission Dynamics of Fractional Order Brucellosis Model Using CaputoFabrizio Operator. Int J Differ Equ 2020;2020:2791380.
  • [21] Peter OJ, Shaikh AS, Ibrahim MO, Nisar KS, Baleanu D, Khan I, Abioye AI. Analysis and dynamics of fractional order mathematical model of COVID-19 in Nigeria using Atangana-Baleanu operator. Comput Mater Continua. 2021;66:18231848.
  • [22] Peter OJ, Yusuf A, Oshinubi K, Oguntolu PA, Ibrahim AA, Abioye AI, Ayoola TA. Fractional order of pneumococcal pneumonia ınfection model with caputo fabrizio operator. Results Phys 2021;29: 104581.
  • [23] Somjaiwang D, Ngiamsunthorn PS. Existence and approximation of solutions to fractional order hybrid differential equations. Adv Differ Equ 2016;2016:278.
  • [24] Tariboon J, Ntouyas SK, Agarwal P. New concepts of fractional quantum calculus and applications to impulsive fractional q-difference equations. Adv Differ Equ 2015;2015:18.
  • [25] Ahmed I, Kumam P, Jarad F, Jirakitpuwapat W. On Hilfer generalized proportional fractional derivative. Adv Differ Equ. 2020;2020:329.
  • [26] Ahmed I, Kumam P, Abubakar J, Borisut P, Sitthithakerngkiet K. Solutions for impulsive fractional pantograph differential equation via generalized anti- periodic boundary condition. Adv Differ Equ 2020;2020:1-15.
  • [27] Borisut P, Kumam P, Ahmed I, Sitthithakerngkiet K. Positive solution for nonlinear fractional differential equation with non-local multi-point condition. Fixed Point Theory 2020;21(2):427-440.
  • [28] Ahmed I, Yusuf A, Sani MA, Jarad F, Kumam W, Thounthong P. Analysis of a Caputo Hiv and Malaria co-infection Epidemic Model. Thai J Math 2021;19:897- 912.
  • [29] Mallah I, Ahmed I, Akgul A, Jarad F, Alha S. On ψ-Hilfer generalized proportional fractional operators. AIMS Mathematics. 2021;7:82-103.
  • [30] Borisut P, Kumam P, Ahmed I, Jirakitpuwapat W. Existence and uniqueness for ψ-Hilfer fractional differential equation with non-local multipoint condition. Math Methods Appl Sci. 2021;44:2506-2520.
There are 31 citations in total.

Details

Primary Language English
Subjects Structural Biology
Journal Section Research Articles
Authors

Norravich Limpanukorn This is me 0000-0001-9350-0271

Idris Ahmed 0000-0003-0901-1673

Muhammad Jamilu Ibrahim This is me 0009-0004-3381-4593

Publication Date April 30, 2024
Submission Date November 2, 2021
Published in Issue Year 2024 Volume: 42 Issue: 2

Cite

Vancouver Limpanukorn N, Ahmed I, Ibrahim MJ. On ψ-quantum fractional operators: Existence, uniqueness and Ulam-Hyers stability. SIGMA. 2024;42(2):313-20.

IMPORTANT NOTE: JOURNAL SUBMISSION LINK https://eds.yildiz.edu.tr/sigma/