International Journal of Mathematics Trends and Technology
Volume 68 | Issue 2 | Year 2022 | Article Id. IJMTT-V68I2P515 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I2P515
Banach space is a finished standard space, which implies that each Cauchy succession of the components of this space closes inside the actual space, and this is the thing that makes it a shut space It also has many applications in functional analysis. The aim of this paper is design and develop highly efficient algorithms that provide the existence of unique solutions to the differential equation in Banach spaces using MATLAB. The quality algorithm was used and developed to solve the differential equation in Banach spaces. For accurate results. The proposed model contributed to providing an integrated computer solution for all stages of the solution starting from the stage of solving differential equations in Banach space and the stage of displaying and representing the results graphically in the MATLAB program. This was done by solving three different types in type and rank to reach accurate readings that provide an ideal model applicable in many of the techniques that contribute to solving our daily problems. This study was distorted in the accuracy of the results with their comparisons from their platforms in the stages and type of solution, as the model achieved high accuracy in the presence of unique solutions to the differential equation in Banach spaces in a computerized form.
[1] G. Teschl, Topics in real and functional analysis, unpublished, available online at http://www. mat. univie. ac. at/~ gerald, (1998).
[2] R. Haloi, D. Bahuguna, and D. N. Pandey, Existence and uniqueness of solutions for quasi-linear differential equations with deviating arguments, Electronic Journal of Differential Equations, 2012(13) (2012) 1-10.
[3] H. Ngo Van and V. Ho, A Study of Fractional Differential Equation with a Positive Constant Coefficient via Hilfer Fractional Derivative, Mathematical Problems in Engineering,. 2020( 2020).
[4] A. B. algebra is a Banach, Banach space.
[5] M. A. Ramadan, H. S. Osheba, and A. R. Hadhoud, A Highly Efficient and Accurate Finite Iterative Method for Solving Linear Two-Dimensional Fredholm Fuzzy Integral Equations of the Second Kind using Triangular functions, Mathematical Problems in Engineering, 2020(2020).
[6] O. Bazighifan and H. Ahmad, Asymptotic Behavior of Solutions of Even-order Advanced Differential Equations, Mathematical Problems in Engineering, vol. 2020(2020).
[7] Y. I. Alber and S. Guerre-Delabriere, Principle of Weakly Contractive Maps in Hilbert Spaces, in New results in Operator theory and its Applications: Springer, (1997) 7-22.
[8] F. Cafiero, Sui teoremi di Unicità Relativi al un’equazione Differenziale Ordinaria del primo Ordine, Ibidem, 78(1948) 10-41.
[9] V. Moauro, S. Leela, and V. Lakshmikantham, Existence and Uniqueness of Solutions of Delay Differential Equations on a Closed Subset of a Banach space, University of Texas at Arlington, (1977).
[10] S. Szufla, On the equation x′= f (t, x) in locally convex spaces, Mathematische Nachrichten, 118(1) (1984) 179-185.
[11] V. Lakshmikantham and S. Leela, Differential and Integral Inequalities: Theory and Applications: Volume I: Ordinary Differential Equations. Academic press, (1969).
[12] J. Horváth, A. Grothendieck, Topological Vector Spaces, Bulletin of the American Mathematical Society, 82(4) (1976) 515-521.
[13] I. Kubiaczyk and S. Szufla, Kneser’s theorem for weak solutions of ordinary differential equations in Banach spaces, Publ. Inst. Math.(Beograd)(NS), 32(46) (1982) 99-103.
[14] T. Kato, Nonlinear semigroups and evolution equations, Journal of the Mathematical Society of Japan, 19(4) (1967) 508-520.
[15] C. Chidume and S. Aneke, Existence, uniqueness and approximation of a solution for a K-positive definite operator equation, Applicable Analysis, 50(3-4) (1993) 285-294.
Abdel Radi Abdel Rahman Abdel Gadir Abdel Rahman, Siham Salih Ahmed Suliman, Hassan Abdelrhman Mohammed Elnaeem, Sulima Ahmed Mohammed Zubir, Subhi Abdalazim Aljily Osman, "Existence and Uniqueness Solutions of Differential Equations in Banach Spaces by Using Matlab," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 2, pp. 95-103, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I2P515
PDF 
Abstract 
Keywords 
References 
Citation