Abdou, M., Soliman, A., Abdalla, M., Gawish, F., Mosa, G. (2020). On Existence and Uniqueness of Fractional Linear Integro Partial Differential Equation with Evolution Kernel Using Modified Bielecki Method and its Numerical Solution. test, 5(Issue 7 part (1) - (2)), 175-181. doi: 10.21608/bjas.2020.226976
M.A. Abdou; A.A. Soliman; M.H. Abdalla; F.A. Gawish; G.A. Mosa. "On Existence and Uniqueness of Fractional Linear Integro Partial Differential Equation with Evolution Kernel Using Modified Bielecki Method and its Numerical Solution". test, 5, Issue 7 part (1) - (2), 2020, 175-181. doi: 10.21608/bjas.2020.226976
Abdou, M., Soliman, A., Abdalla, M., Gawish, F., Mosa, G. (2020). 'On Existence and Uniqueness of Fractional Linear Integro Partial Differential Equation with Evolution Kernel Using Modified Bielecki Method and its Numerical Solution', test, 5(Issue 7 part (1) - (2)), pp. 175-181. doi: 10.21608/bjas.2020.226976
Abdou, M., Soliman, A., Abdalla, M., Gawish, F., Mosa, G. On Existence and Uniqueness of Fractional Linear Integro Partial Differential Equation with Evolution Kernel Using Modified Bielecki Method and its Numerical Solution. test, 2020; 5(Issue 7 part (1) - (2)): 175-181. doi: 10.21608/bjas.2020.226976

On Existence and Uniqueness of Fractional Linear Integro Partial Differential Equation with Evolution Kernel Using Modified Bielecki Method and its Numerical Solution

Benha Journal of Applied Sciences
Article 29, Volume 5, Issue 7 part (1) - (2), October 2020, Pages 175-181    PDF (464.14 K)
Document Type: Original Research Papers
DOI: 10.21608/bjas.2020.226976
Authors
M.A. Abdou1; A.A. Soliman2; M.H. Abdalla2; F.A. Gawish2; G.A. Mosa2
1Mathematics Dept., Faculty of Education, Alexandria Univ., Benha, Egypt
2Mathematics Dept., Faculty of Science, Benha Univ., Benha, Egypt
Abstract
The devote of this paper is discussing the existence and uniqueness of fractional linear integro partial differential equation with
evolution kernel of heat type due to modified Bielecki method. In addition, Laplace homotopy perturbation method is used to
obtain the numerical solutions in the space 𝐢𝐸(𝐸 × [0, 𝑇]). Therefore, we estimate the error in different cases of 𝛼.
Keywords
Fractional linear integro partial differential equation (FLIPDE); Caputo derivative; Riemann integral; Modified Bielecki method; Laplace homotopy perturbation method (LHPM)
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