On Existence and Uniqueness of Fractional Linear Integro Partial Differential Equation with Evolution Kernel Using Modified Bielecki Method and its Numerical Solution
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. EKB Journal Management System, 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". EKB Journal Management System, 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', EKB Journal Management System, 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. EKB Journal Management System, 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, Page 175-181  XML PDF (464.14 K)
Document Type: Original Research Papers
DOI: 10.21608/bjas.2020.226976
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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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