
تعداد نشریات | 21 |
تعداد شمارهها | 608 |
تعداد مقالات | 9,002 |
تعداد مشاهده مقاله | 67,038,969 |
تعداد دریافت فایل اصل مقاله | 7,622,212 |
Solvability of infinite systems of fractional differential equations in the space of tempered sequence space $m^\beta(\phi)$ | ||
International Journal of Nonlinear Analysis and Applications | ||
مقاله 85، دوره 13، شماره 1، خرداد 2022، صفحه 1023-1034 اصل مقاله (421.35 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.23299.2515 | ||
نویسندگان | ||
Hamid Mehravaran؛ Hojjatollah Amiri Kayvanloo؛ Reza Allahyari* | ||
Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran. | ||
تاریخ دریافت: 09 اردیبهشت 1400، تاریخ بازنگری: 15 شهریور 1400، تاریخ پذیرش: 24 شهریور 1400 | ||
چکیده | ||
The purpose of this article, is to establish the existence of solution of infinite systems of fractional differential equations in space of tempered sequence $m^\beta(\phi)$ by using techniques associated with Hausdorff measures of noncompactness. Finally, we provide an example to highlight and establish the importance of our main result. | ||
کلیدواژهها | ||
Fractional differential equations؛ Hausdorff measure of noncompactness؛ Meir-Keeler condensing operator؛ Space of tempered sequence | ||
مراجع | ||
[1] A. Aghajani, J. Bana´s and Y. Jalilian, Existence of solution for a class of nonlinear Volterra singular integral equation, Comput. Math. Appl. , 62 (2011) 1215-1227. [2] A. Aghajani, M. Mursaleen and A. Shole Haghighi, Fixed point theorems for Meir–Keeler condensing operators via measure of noncompactness, Acta Math. Sci. , 35B(3) (2015) 552–566. [3] A. Aghajani, E. Pourhadi and J.J. Trujillo, Application of measure of noncompactness to a Cauchy problem for fractional differential equation in Banach spaces, Fract. Calc. Appl. Anal., 16(4) (2003) 962—977. [4] R. Arab, R. Allahyari and A. Shole Haghighi, Existence of solutions of infinite systems of integral equations in two variables via measure of noncompactness, Appl. Math. Comput., 246 (2014) 283-291. [5] J. Bana´s and K. Goebel, Measure of noncompactness in Banach spaces, Lecture notes in pure and applied mathematics. vol. 60. New York: Marcel Dekker, (1980). [6] J. Bana´s and D. O’Regan, On existence and local attractivity of solutions of a quadratic Volterra integral equation of fraction order, J. Math. Anal. Appl. , 345 (2008) 573-582. [7] J. Bana´s M. and Mursaleen, Sequence spaces and measures of noncompactness with applications to differential and integral equations, New Delhi: Springer, 2014. [8] E. Cuesta and J.F Codes, Image processing by means of a linear integro differential equation Visualization imaging and image processing (2003), paper 91, Clagary, (2003). Hamza MH, editor. Acta Press. [9] G. Darbo, Punti uniti in trasformazioni a codominio non compatto, Rend Sem Mat Univ Padova., 24 (1955) 84–92. [10] W. Deng, Short memory principal and a predictor-corrector approach for fractional differential equations, J. Comput. Appl. Math., 206 (2007) 174–188. [11] K. Diethelm, The analysis of fractional differential equations An application-oriented exposition using differential operators of Caputo type, Springer Science Business Media (2010). [12] L.S. Goldenˇstein, L.T. Gohberg and A.S. Murkus, Investigations of some properties of bounded linear operators with their q-norms, Uˇcen. Zap. Kishinevsk. Uni. , 29 (1957) 29-36. [13] L.S. Goldenˇstein and A.S. Murkus, On a measure of noncompactness of bounded sets and linear operators, Studies in Algebra and Math. Anal. Kishinev, (1965) 45-54. [14] B. Hazarika, E. Karapınar, R. Arab and M. Rabbani, Metric-like spaces to prove existence of solution for nonlinear quadratic integral equation and numerical method to solve it, J. Comput. Appl. Math., 328 (15)(2018) 302–313. [15] A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science Publishers, vol. 204, 2006. [16] K. Kuratowski, Sur les espaces complets, Fund. Math., 15 (1930) 301-309. [17] K. Maleknejad, P. Torabi and R. Mollapourasl, Fixed point method for solving nonlinear quadratic Volterra integral equations, Comput. Math. Appl., 62 (2011) 2555-2566. [18] A. Meir and E.A. Keeler, Theorem on contraction mappings, J. Math. Anal. Appl., 28 (1969) 326–329. [19] M. Mursaleen, Application of measure of noncompactness to infinite system of differential equations, Canad. Math. Bull., 56 (2013) 388-394. [20] M. Mursaleen, Some geometric properties of a sequence space related to lp, Bull. Austral. Math. Soc. , 67 (2003) 343-347. [21] M. Mursaleen, Differential equations in classical sequence spaces, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM, 111(2) (2017) 587–612. [22] M. Mursaleen and A. Alotaibi, Infinite system of differential equations in some BK spaces, Abstract Appl. Anal., Volume 2012, Article ID 863483, 20 pages. [23] M. Mursaleen, B. Bilalov and S.M.H. Rizvi, Applications of measure of noncompactness to infinite system of fractional differential equations, Filomat. 31 (11) (2017) 3421–3432. [24] I. Podlubny, Fractional order systems and fractional order controllers, Technical report of-03-94. Institute of Experimental Physics, Slovak Acad. of Sci.; (1994). [25] I. Podlubny, Fractional Differential Equations An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, Elsevier, vol. 198, 1998. [26] M. Rabbani, A. Das, B. Hazarika and R. Arab, Measure of noncompactness of a new space of tempered sequences and its application on fractional differential equations, Chaos, Solitons and Fractals 140 (2020) 110221. [27] W.L.C Sargent, Some sequence spaces related to the HP spaces, J. London Math. Soc. 35 (1960) 161-171. | ||
آمار تعداد مشاهده مقاله: 15,929 تعداد دریافت فایل اصل مقاله: 531 |