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Existence and stability of solutions for a nonlinear fractional Volterra-Fredholm integro-differential equation in Banach spaces | ||
Journal of Mahani Mathematical Research | ||
دوره 10، شماره 1، مرداد 2021، صفحه 79-93 اصل مقاله (472.14 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22103/jmmrc.2021.17079.1130 | ||
نویسندگان | ||
Ahmed A Hamoud* 1؛ Abdulrahman A. Sharif2؛ Kirtiwant Ghadle3 | ||
1Taiz University | ||
2Department of MathematicsHodeidah UniversityAl-Hudaydah, Yemen. | ||
3Dr. Babasaheb Ambedkar Marathwada University | ||
چکیده | ||
This paper investigates the existence and interval of existence, uniqueness and Ulam stability of solutions on initial value type problem of a nonlinear Caputo fractional Volterra-Fredholm integro-differential equation in Banach spaces. | ||
کلیدواژهها | ||
Fractional Volterra-Fredholm integro-differential equation؛ Caputo sense؛ Fixed point technique | ||
مراجع | ||
[1] B. Ahmad and S. Sivasundaram, Some existence results for fractional integro-dierential equations with nonlinear conditions, Communications Appl. Anal., Vol.12 (2008), 107- 112. [2] D. Bahuguna and J. Dabas, Existence and uniqueness of a solution to a partial integro- dierential equation by the method of Lines, Electronic Journal of Qualitative Theory of Dierential Equations, Vol.4 (2008), 1-12. [3] K. Balachandran, J. J. Trujillo, The nonlocal Cauchy problem for nonlinear fractional integro-dierential equations in Banach spaces, Nonlinear Anal. Theory Meth. Applic., Vol.72 (2010), 4587-4593. [4] J. Devi and Ch. Sreedhar, Generalized monotone iterative method for Caputo fractional integro-dierential equations, Eur. J. Pure Appl. Math. Vol.9, No.4 (2016), 346-359. [5] A. Hamoud and K. Ghadle, The approximate solutions of fractional Volterra-Fredholm integro-dierential equations by using analytical techniques, Probl. Anal. Issues Anal., Vol.7 (25) (2018), 41-58. [6] A. Hamoud and K. Ghadle, Modied Laplace decomposition method for fractional Volterra-Fredholm integro-dierential equations, J. Math. Model., Vol.6 (2018), 91-104. [7] A. Hamoud and K. Ghadle, Usage of the homotopy analysis method for solving fractional Volterra-Fredholm integro-dierential equation of the second kind, Tamkang J. Math. Vol.49 (2018), 301-315. [8] A. Hamoud, K. Hussain and K. Ghadle, The reliable modied Laplace Adomian de- composition method to solve fractional Volterra-Fredholm integro-dierential equations, Dynamics of Continuous, Discrete and Impulsive Systems, Series B: Applications and Algorithms, Vol.26 (2019), 171-184. [9] A. Hamoud and K. Ghadle, Existence and uniqueness of solutions for fractional mixed Volterra-Fredholm integro-dierential equations, Indian J. Math. Vol.60 (2018), 375-395. [10] A. Hamoud, K. Ghadle, M. Bani Issa and Giniswamy, Existence and uniqueness theo- rems for fractional Volterra-Fredholm integro-dierential equations, Int. J. Appl. Math. Vol.31 (2018), 333-348. [11] A. Hamoud, K. Ghadle and S. Atshan, The approximate solutions of fractional integro- dierential equations by using modied Adomian decomposition method, Khayyam J. Math. Vol.5 (2019), 21-39. [12] A. Hamoud and K. Ghadle, Some new existence, uniqueness and convergence results for fractional Volterra-Fredholm integro-dierential equations, J. Appl. Comput. Mech. Vol.5 (2019), 58-69. [13] A. Hamoud, Existence and uniqueness of solutions for fractional neutral Volterra- Fredholm integro-dierential equations, Advances in the Theory of Nonlinear Analysis and its Application, Vol.4, No.4 (2020), 321-331. [14] A. Hamoud, N. Mohammed and K. Ghadle, Existence and uniqueness results for Volterra-Fredholm integro-dierential equations, Advances in the Theory of Nonlinear Analysis and its Application, Vol.4, No.4 (2020), 361-372. [15] R. Ibrahim and S. Momani, On the existence and uniqueness of solutions of a class of fractional dierential equations, Journal of Mathematical Analysis and Applications, Vol.334 (2007), 1-10. [16] K. Logeswari, and C. Ravichandran, A new exploration on existence of fractional neutral integro-dierential equations in the concept of Atangana-Baleanu derivative, Physica A: Statistical Mechanics and Its Applications, Vol.544 (2020), 1-10. [17] S. Momani, A. Jameel and S. Al-Azawi, Local and global uniqueness theorems on fractional integro-dierential equations via Bihari's and Gronwall's inequalities, Soochow Journal of Mathematics, 33(4), (2007) 619-627. [18] S. M. Momani, Local and global uniqueness theorems on dierential equations of non- integer order via Bihari's and Gronwall's inequalities, Revista Tecnica J., Vol.23 (2000), 66-69. [19] K. Karthikeyan and J. Trujillo, Existence and uniqueness results for fractional integro- dierential equations with boundary value conditions, Commun. Nonlinear Sci. Numer. Simulat., Vol.17 (2012), 4037-4043. [20] A. Khan, H. Khan, J.F. Gomez-Aguilar, T. Abdeljawad, Existence and Hyers-Ulam stability for a nonlinear singular fractional dierential equations with Mittag-Leer kernel, Chaos Solitons Fractals, Vol.127 (2019), 422-427. [21] A. Kilbas, H. Srivastava and J. Trujillo, Theory and Applications of Fractional Dier- ential Equations, North-Holland Math. Stud. Elsevier, Amsterdam, 2006. [22] V. Lakshmikantham and M. Rao, Theory of Integro-Dierential Equations, Gordon and Breach, London, 1995. [23] M. Matar, Controllability of fractional semilinear mixed Volterra-Fredholm integro- dierential equations with nonlocal conditions, Int. J. Math. Anal., Vol.4 (2010), 1105- 1116. [24] K. Miller and B. Ross, An Introduction to the Fractional Calculus and Dierential Equations, John Wiley, New York, 1993. [25] B. Pachpatte, Inequalities for dierential and integral equations, Academic Press, New York, 1998. [26] S. Samko, A. Kilbas and O. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, 1993. [27] S. Tate, V. Kharat and h. Dinde, On nonlinear fractional integro-dierential equations with positive constant coecient, Mediterranean Journal of Mathematics, Vol.16 (2019), 1-20. [28] J. Wu and Y. Liu, Existence and uniqueness of solutions for the fractional integro- dierential equations in Banach spaces, Electronic Journal of Dierential Equations, Vol.2009 (2009), 1-8. | ||
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