On a Class of Caputo Time Fractional Problems with Boundary Integral Conditions

Karim Aggoun; Ahcene Merad

doi:10.2478/mjpaa-2021-0027

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On a Class of Caputo Time Fractional Problems with Boundary Integral Conditions

Moroccan Journal of Pure and Applied Analysis

Volume 7 (2021): Issue 3 (September 2021)

By: Karim Aggoun and Ahcene Merad

Open Access

|Apr 2021

Abstract

The aim of this paper is to work out the solvability of a class of Caputo time fractional problems with boundary integral conditions. A generalized formula of integration is demonstrated and applied to establish the a priori estimate of the solution, then we prove the existence which is based on the range density of the operator associated with the problem.

References

[1] A.A. Alikhanov, A priori estimates for solutions of boundary value problems for fractional-order equations, Differential Equations, Vol. 46, No. 5, pp. 660–666, 2010. https://doi.org/10.1134/S001226611005005810.1134/S0012266110050058
Search in Google Scholar Back to article
[2] A. Bouziani, Mixed problem with boundary integral conditions for a certain parabolic equation, Journal of Applied Mathematics and Stochastic Analysis, vol. 9, no. 3, pp. 323–330, 1996. https://doi.org/10.1155/S104895339600030510.1155/S1048953396000305
Search in Google Scholar Back to article
[3] A. Bouziani,Initial boundary value problem with a non-local condition for a viscosity equation, Hindawi Publishing Corp, Vol 30, No.6, pp. 327–338, 2002. https://doi.org/10.1155/S016117120200416710.1155/S0161171202004167
Search in Google Scholar Back to article
[4] A.L. Marhoune and C. Latrous, A strong solution of a high-order mixed type partial differential equation with integral conditions, Applicable Analysis,Vol. 87, No. 6, pp. 625–634, 2008.10.1080/00036810802091660
Search in Google Scholar Back to article
[5] A. Merad, A.L. Marhoune, Strong solution for a high order boundary value problem with integral condition, Turkish Journal of Mathematics 37 (2), 299-307, 2013. https://doi.org/10.3906/mat-1105-3410.3906/mat-1105-34
Search in Google Scholar Back to article
[6] A. Merad, J. Martin-Vaquero, A Galerkin method for two-dimensional hyperbolic integro-differential equation with purely integral conditions, Applied Mathematics and Computation, Vol 291, pp. 386–394, 2016. https://doi.org/10.1016/j.amc.2016.07.00310.1016/j.amc.2016.07.003
Search in Google Scholar Back to article
[7] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
Search in Google Scholar Back to article
[8] J. Martin-Vaqueroa, A. Merad, Existence, uniqueness and numerical solution of a fractional PDE with integral conditions, Nonlinear Analysis: Modelling and Control, Vol. 24, No. 3, pp. 368–386, 2019. https://doi.org/10.15388/NA.2019.3.410.15388/NA.2019.3.4
Search in Google Scholar Back to article