| Keywords and phrases: Some Blaise Abbo (SBA) method, Hadamard fractional integral, Caputo-Hadamard fractional derivative, Caputo-Hadamard fractional evolution equations.
Received: September 25, 2023; Accepted: November 21, 2023; Published: January 8, 2024
How to cite this article: Germain KABORE, Bakari Abbo, Windjiré SOME, Ousséni SO and Blaise SOME, Solving a fractional evolution equation in the sense of Caputo-Hadamard with Cauchy and boundary conditions by SBA method, Advances in Differential Equations and Control Processes 31(1) (2024), 1-14. http://dx.doi.org/10.17654/0974324324001
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License  
References:
[1] Abdelaziz OUALID, Équations Différentielles au Sens de Hadamard, Université Abdelhamid Ben Badis dde Mostaganem, Master soutenu, 2018.
[2] Abdoul wassiha NEBIE, Frédéric BERE, Bakari ABBO and Youssouf PARE, Solving some derivative equations fractional order nonlinear partials using the some Blaise Abbo method, Journal of Mathematics Research 13(2) (2021). doi: 10.5539/jmr.v13n2p101.
[3] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Vol. 204, Elsevier Science Limited, Amsterdam, Netherlands, 2006.
[4] B. ABBO, O. SO, G. BARRO and B. SOME, A new numerical algorithm for solving nonlinear partial differential equations with initial and boundary conditions, Far East J. Appl. Math. 28(1) (2007), 37-52.
[5] Blaise SOME, Méthode SBA de résolution des modèles mathématiques en environnement, Éditions Universitaires Européennes, 2018.
[6] B. Abbo, Nouvel algorithme numérique de résolution des équations différentielles ordinaries (EDO) et des équations aux dérivées partielles (EDP) non linéaires, Thèse de Doctorat unique, Université de Ouagadougou, UFR/ SEA, Département Mathématique et Informatique, Burkina Faso, 2007.
[7] C. Young, G. Farid, S. Ullah, W. Nazeer, K. Mahreen and M. Shin, Inequalities for a unified integral operator and associated results in fractional calculus, IEEE Access 7 (2019), 126283-126292.
[8] G. KABORE, W. SOME, M. KÉRÉ, O. SO and B. SOME, Solving some fractional ordinary differential equations by SBA method, Journal of Mathematics Research 15(1) (2023). doi: 10.5539/jmr.v15n1p47.
[9] Germain KABORE, KÉRÉ Moumini, Windjiré SOME, Ousséni SO and Blaise SOME, Solving some fractional equations, in the sense of Riemann-Liouville, of Navier-Stokes by the numerical method SBA plus, International Journal of Numerical Methods and Applications 23(2) (2023), 209-228.
http://dx.doi.org/10.17654/0975045223012.
[10] F. Jarad, T. Abdeljawad and D. Baleanu, Caputo-type modification of the Hadamard fractional derivatives, Adv. Difference Equ. (2012), Article number 142. doi: 10.1186/1687-1847-2012-142.
[11] J. Hadamarad, Essai sur l’etude des fonctions données par leur développment de Taylor, J. Pure Appl. Math. 4(8) (1892), 101-186.
[12] Mountassir Hamdi Cherif, Résolution numérique des équations différentielles et aux dérivées partielles non linéaire et d’ordre fractionnaire par la méthode HPM, Thèse de Doctorat, Université d’ORAN 1, AHMED BEN BELLA, Soutenue le 17/05/2016.
[13] Houmor Tarek, Analyse du chaos dans un système d’équations différentielles fractionnaires, Thèse soutenue le 30/09/2014, Université Constantine 1.
[14] H. R. Marasi and H. Aydi, Existence and uniqueness results for two-term nonlinear fractional differential equations via a fixed point technique, J. Math. Volume 2021, Article ID 6670176, 7 pp. https://doi.org/10.1155/2021/6670176.
[15] I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Deir Solution and Some of Deir Applications, Elsevier, Amsterdam, Netherlands, 1998.
[16] Kamate Adama, Bationo Jeremie Yiyureboula, Djibet Mbaiguesse and Youssouf Pare, Analytica l solutions of classical and fractional Navier-Stokes equations by the SBA method, Journal of Mathematics Research 14(4) (2022), 1-20.
https://doi.org/10.5539/jmr.v14n4p20.
[17] Khalouta Ali, Résolution des équations aux dérivées partielles linéaires et non-linéaires moyennant des approches analytiques, Extension aux cas d’EDP d’ordre fractionnaire, Thèse de doctorat de l’Université Ferhat ABBAS SETIF1, 2019.
[18] M. Shin, G. Farid, W. Nazeer and S. Mehmood, (h-m)-convex functions and associated fractional Hadamard and Fejer-Hadamard inequalities via an extended generalized Mittag-Leffler function, J. Inequal. Appl. (2019), Paper No. 78, 10 pp.
[19] M. Shin, G. Farid, W. Nazeer and B. Tariq, Hadamard and Fejer-Hadamard inequalities for extended generalized fractional integrals involving special functions, Journal of Inequalities and Applications 2018(1) (2018), 119.
[20] P. Thiramanus, S. K. Ntouyas and J. Tariboon, Existence and uniqueness results for Hadamard-type fractional differential equations with nonlocal fractional integral boundary conditions, Abstr. Appl. Anal. Vol. 2014, Article ID 902054, 9 pp. http://dx.doi.org/10.1155/2014/902054.
[21] S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives - Theory and Applications, Gordon & Breach, Langhorne, 1993.
[22] S. N. Rao, A. H. Msmali, M. Singh and A. A. H. Ahmadini, Existence and uniqueness for a system of Caputo-Hadamard fractional differential equations with multipoint boundary conditions, Journal of Function Spaces Vol. 2020 (2020), Article ID 8821471, 10 pp. https://doi.org/10.1155/2020/8821471.
[23] S. Zhao, S. I. Butt, W. Nazeer, J. Nasir, M. Umar and Y. Liu, Some Hermite Jensen-Mercer type inequalities for k-Caputo-fractional derivatives and related results, Adv. Difference Equ. 2020(1) (2020), 1-17.
[24] Zaid Laadjal, Etude de Quelques Problemes aux Limites Non Lineaires D’ordre Fractionnaire, Université Abbès Laghrour-Khenchela, Thèse soutenue, 2021.
|
