Analytic and Numeric Solution of Linear Partial Differential Equation of Fractional Order

maha mko

Authors

maha mko

linear partial differential equation of fractional order, semigroup, linear algebraic system, product nyström method

Abstract

The existence and uniqueness solution of the Cauchy problem are discussed and proved in a Banach space E due to Bielecki method and Picard method depending on the properties we expect a solution to possess. Moreover, some properties concerning the stability of solution are obtained. The product Nyström method is used as a numerical method to obtain a linear system of algebraic equations. Also, many important theorems related to the existence and uniqueness solution of the algebraic system are derived. Finally, an application is given and numerical results are obtained.

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How to Cite

Analytic and Numeric Solution of Linear Partial Differential Equation of Fractional Order. (2013). Global Journal of Science Frontier Research, 13(12), 57-71. https://journalofscience.org/index.php/GJSFR/article/view/

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Author Biography

maha mko

Dr. Sameeha Ali is an applied mathematician and academic currently serving as an Associate Professor in the Department of Mathematical Sciences at Umm Al-Qura University in Makkah, Saudi Arabia. She earned her Ph.D. in Applied Mathematics (Integral Equations and Elasticity) from Umm Al-Qura University, following an MSc in Applied Mathematics (Integral Equations and Numerical Analysis) from the same institution, and a Bachelor's Degree in Mathematics from King Abdulaziz University. Her research interests include integral equations, fractional differential equations, and numerical analysis. Dr. Ali has published 14 scholarly works, accumulating 36 citations and an h-index of 4. She has previously held positions at Alexandria University and Qassim University, contributing to the field of applied mathematics through her teaching and research.

References

W. Feller THE PARABOLIC DIFFERENTIAL EQUATIONS AND THE ASSOCIATED SEMI-GROUPS OF TRANSFORMATIONS.

transformations (1952) 55, 468-519.

(1950) 10th Congress of Scandinavian Mathematics.

K. Yosida, An process (1949) An operator process. 1, 244-homogeneous Markoff 253.

S. Chandrasekhar, G. Münch (1974) (1974).

Michael Mackey, Ryszard Rudnicki (1994) Global stability in a delayed partial differential equation describing cellular replication. 33(1), 89-109. https://doi.org/10.1007/bf00160175

(1986) Populations" Springer lecture Notes in Biomathematics. 68.

Mahmoud EL-Borai (1997) Some probability densities and fundamental solutions of fractional evolution equations. 14(3), 433-440. https://doi.org/10.1016/s0960-0779(01)00208-9

Mahmoud El-Borai (2004) Semigroups and some nonlinear fractional differential equations. 149(3), 823-831. https://doi.org/10.1016/s0096-3003(03)00188-7