Numerical Solution For Systems Of Fractional Initial Value Problems - Mathewos Gizaw (ASTU, 2023)
This Thesis Presents A Numerical Solution For Systems Of Fractional Initial Value Problems (Sfivps. It Playa Crucial Role In Various Scientific And Engineering Fields, Offering More Accurate Models For Real-World Phe Nomena Involving Memory And Hereditary Effects. To Address These Challenges, The Thesis Employs The L3 Type Caputo Method, A Powerful Numerical Technique For Solving Sfivps. Additionally, The Fractional Finite Differ Ence Method (Ffdm) Is Utilized For Discretizing The System. The L3 Type Caputo Method Is Applied To Find The Numerical Solutions For Such Sfivps. Lipschitz Continuity Is The Main Condition For Picard-Lindel??F ??S The Oremthat Guarantees The Existence And Uniqueness Of A System Of Fractional Initial Value Problems Depending Onthe Given Discretization. Moreover, We Investigate The Consistency, Stability, And Convergence Properties Of The Proposed Method. Stability Analysis Is Performed To Examine The Behavior Of The L3 Caput
Keywords: Fractional Initial Value Problem; Systems Of Fractional Initial Value Problem; Fractional Fi Nite Difference Method; Fractional Calculus; Stability Analysis.