110
Views
1
CrossRef citations to date
0
Altmetric
Research Article

The explicit solutions for a class of fractional Fourier–Laplace convolution equations

ORCID Icon & ORCID Icon
Pages 128-144 | Received 06 Dec 2021, Accepted 21 Jun 2022, Published online: 19 Jul 2022

References

  • Jakubowski J, Wisniewolski M. Explicit solutions of Volterra integro-differential convolution equations. J Differ Equ. 2021;292:416–426.
  • Dilnyi V. Solvability criterion for convolution equations on a half-strip. Complex Anal. Oper. Theory. 2021;15(4):1–13.
  • Goodrich CS. Nonlocal differential equations with concave coefficients of convolution type. Nonlinear Anal. 2021;211:1–18.
  • Li ZW, Gao WB, Li BZ. The solvability of a class of convolution equations associated with 2D FRFT. Mathematics. 2020;8(11):1928–1940.
  • Castro LP, Goel N, Silva AS. A new convolution operator for the linear canonical transform with applications. Comput Appl Math. 2021;43(3):1–18.
  • Castro LP, Guerra RC, Tuan NM. New convolutions and their applicability to integral equations of Wiener-Hopf plus Hankel type. Comput Appl Math. 2020;43(3):4835–4846.
  • Maslakov ML. Application of two-parameter stabilizing functions in solving a convolution-type integral equation by regularization method. Comput Math Math Phys. 2018;58(4):529–536.
  • Futcher T, Rodrigo MR. A general class of integral transforms and an expression for their convolution formulas. Integral Transforms Spec Funct. 2022;33(2):91–107.
  • Wen ZS, Li HJ, Fu YG. Abundant explicit periodic wave solutions and their limit forms to space-time fractional Drinfel'd-Sokolov-Wilson equation. Math Methods Appl Sci. 2021;44(8):6406–6421.
  • Feng Q, Wang RB. Fractional convolution associated with a class of integral equations. IET Signal Process. 2020;14(1):15–23.
  • Li PR. Singular integral equations of convolution type with reflection and translation shifts. Numer Funct Anal Optim. 2019;40(9):1023–1038.
  • Nguyen MT, Nguyen TTH. The solvability and explicit solutions of two integral equations via generalized convolutions. J Math Anal Appl. 2010;369(2):712–718.
  • Thao NX, Tuan VK, Huy LX, et al. On the Fourier-Laplace convolution transforms. Integral Transforms Spec Funct. 2015;26(4):303–313.
  • Castro LP, Guerra RC, Tuan NM. New convolutions weighted by Hermite functions and their applications. Math Inequal Appl. 2019;22(2):719–745.
  • Castro LP, Minh LT, Tuan NM. New convolutions for quadratic-phase Fourier integral operators and their applications. Mediterr J Math. 2018;15(1):1–13.
  • Thao NX, Huy LX. Fourier cosine-Laplace generalized convolution inequalities and applications. Math Inequal Appl. 2019;22(1):181–195.
  • Najafabadi FP, Nieto JJ, Kayvanloo HA. Measure of noncompactness on weighted Sobolev space with an application to some nonlinear convolution type integral equations. J Fixed Point Theory Appl. 2020;22(3):1–15.
  • Feng Q, Li BZ. Convolution theorem for fractional cosine-sine transform and its application. Math Methods Appl Sci. 2017;40(10):3651–3665.
  • Li PR. Existence of solutions for dual singular integral equations with convolution kernels in case of non-normal type. J Appl Anal Comput. 2020;10(6):2756–2766.
  • Thao NX, Tuan T, Huy LX. The Fourier-Laplace generalized convolutions and applications to integral equations. Vietnam J Math. 2013;41:451–464.
  • Bui TG, Nguyen MT. Generalized convolutions and the integral equations of the convolution type. Complex Var Elliptic Equ. 2010;55(4):331–345.
  • Thao NX, Kakichev VA, Tuan VK. On the generalized convolutions for Fourier cosine and sine transforms. East West J Math. 1998;1(1):85–90.
  • Thao NX, Tuan VK, Hong NT. A Fourier generalized convolution transform and applications to integral equations. Fract Calc Appl Anal. 2012;15(3):493–508.
  • Namias V. The fractional order Fourier transform and its application to quantum mechanics. IMA J Appl Math. 1980;25(3):241–265.
  • Pei SC, Ding JJ. Fractional cosine, sine, and Hartley transforms. IEEE Trans Signal Process. 2002;50(7):1661–1680.
  • Paley REAC, Wiener N. Fourier transforms in the complex domain. New York (NY): American Mathematical Society; 1934.
  • Schiff JL. The Laplace transforms: theory and applications. New York (NY): Springer-Verlag Inc; 1999.
  • Churchill RV. Fourier series and boundary value problems. New York (NY): McGraw-Hill; 1941.
  • Debnath L, Bhatta D. Integral transforms and their applications. Boca Raton (FL): Chapman and Hall/CRC; 2007.
  • Adams RA, Fournier JJF. Sobolev spaces. 2nd ed. New York (NY): Academic Press; 2003.
  • Guo WC, Fan DS, Wu HX, et al. Sharp weighted convolution inequalities and some applications. Stud Math. 2018;241(3):201–239.
  • Nursultanov E, Tikhonov S. Weighted norm inequalities for convolution and Riesz potential. Potential Anal. 2015;42(2):435–456.
  • Saitoh S. Weighted Lp-norm inequalities in convolutions. In: Rassias TM, editor. Survey on classical inequalities.Amsterdam: Kluwer Academic Publishers; 2000. p. 225–234.
  • Feng Q, Wang RB. Fractional convolution, correlation theorem and its application in filter design. Signal Image Video Process. 2020;14(2):351–358.
  • Wei DY, Li YM. Convolution and multichannel sampling for the offset linear canonical transform and their applications. IEEE Trans Signal Process. 2019;67(23):6009–6024.
  • Nussbaumer HJ. Fast Fourier transform and convolution algorithms. New York (NY): Springer-Verlag; 1981.
  • Naimark MA. Normed algebras. Groningen: Wolters-Noordhoff Publishers; 1972.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.