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The analytical solutions for conformable integral equations and integro-differential equations by conformable Laplace transform

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Abstract

In this article, existence theorem for conformable Laplace transform is expressed. Then by using basic properties of conformable Laplace transform such as convolution theorem, conformable Laplace transform of fractional derivative and fractional integral, authors obtained the exact solution of initial value problems for integral equations and integro-differential equations where the derivatives and integrals are in conformable sense. In the literature it is the first time that obtaining the solutions of integro differential equations, integral equations by means of conformable fractional derivative.

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References

  • Abdeljawad, T.: On conformable fractional calculus. J. Comput. Appl. Math. 279, 57–66 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  • Avci, D., Iskender Eroglu, B.B., Ozdemir, N.: Conformable heat equation on a radial symetric plate. Therm. Sci. 21(2), 819–82 (2017a)

    Article  Google Scholar 

  • Avci, D., Iskender Eroglu, B.B., Ozdemir, N.: The dirichlet problem of a conformable advection-diffusion equation. Therm. Sci. 21(1), 9–18 (2017b)

    Article  Google Scholar 

  • Eroglu, B.I., Avci, D., Ozdemir, N.: Optimal control problem for a conformable fractional heat conduction equation. Acta Phys. Polon. A 132(3), 658–662 (2017)

    Article  Google Scholar 

  • Gulsen, T., Ylmaz, E., Goktas, S.: Conformable fractional Dirac system on time scales. J. Inequal. Appl. 2017, 161 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  • Kaplan, M.: Applications of two reliable methods for solving a nonlinear conformable time-fractional equation. Opt. Quantum Electron. 49, 312 (2017)

    Article  Google Scholar 

  • Khalil, R., Al Horani, M., Yousef, A., Sababheh, M.: A new definition of fractional derivative. J. Comput. Appl. Math. 264, 65–70 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  • Kilbas, A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, San Diego (2006)

    MATH  Google Scholar 

  • Korkmaz, A., Hosseini, K.: Exact solutions of a nonlinear conformable time-fractional parabolic equation with exponential nonlinearity using reliable methods. Opt. Quantum Electron. 49, 278 (2017)

    Article  Google Scholar 

  • Miller, K.S., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York (1993)

    MATH  Google Scholar 

  • Neirameh, A.: New fractional calculus and application to the fractional-order of extended biological population model. Boletim da Sociedade Paranaense de Matemtica 36(3), 115–128 (2018)

    Article  Google Scholar 

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

    MATH  Google Scholar 

  • Zhao, D., Luo, M.: General conformable fractional derivative and its physical interpretation. Calcolo 54, 903 (2017)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Selçuk University, Konya, Turkey

    Ozan Özkan

  2. Department of Mathematics, Mustafa Kemal University, Hatay, Turkey

    Ali Kurt

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  1. Ozan Özkan
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  2. Ali Kurt
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Correspondence to Ali Kurt.

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Özkan, O., Kurt, A. The analytical solutions for conformable integral equations and integro-differential equations by conformable Laplace transform. Opt Quant Electron 50, 81 (2018). https://doi.org/10.1007/s11082-018-1342-2

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  • DOI: https://doi.org/10.1007/s11082-018-1342-2

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