Boundary value problem of weighted fractional derivative of a function with a respect to another function of variable order

被引：0
作者：
Kheireddine Benia
Mohammed Said Souid
Fahd Jarad
Manar A. Alqudah
Thabet Abdeljawad
机构：
[1] Ibn Khaldoun University,Departement of Mathematics
[2] Ibn Khaldoun University,Department of Economic Sciences
[3] Çankaya Univ,Department of Mathematics, Faculty of Arts and Science
[4] Princess Nourah Bint Abdulrahman Univ,Dept Math Sci, Fac Sci
[5] Prince Sultan University,Department of Mathematics and Sciences
[6] China Medical University,Department of Medical Research
[7] Kyung Hee University,Department of Mathematics
[8] Sefako Makgatho Health Sciences University,Department of Mathematics and Applied Mathematics
来源：
Journal of Inequalities and Applications | / 2023卷
关键词：
Weighted fractional integrals; Weighted spaces of summable functions; Fixed point theorem; Derivatives and integrals of variable order; Boundary value problem; Measure of non-compactness; 26A33; 47H08; 34B15; 34A08; 37C25;
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摘要：
This study aims to resolve weighted fractional operators of variable order in specific spaces. We establish an investigation on a boundary value problem of weighted fractional derivative of one function with respect to another variable order function. It is essential to keep in mind that the symmetry of a transformation for differential equations is connected to local solvability, which is synonymous with the existence of solutions. As a consequence, existence requirements for weighted fractional derivative of a function with respect to another function of constant order are necessary. Moreover, the stability with in Ulam–Hyers–Rassias sense is reviewed. The outcomes are derived using the Kuratowski measure of non-compactness. A model illustrates the trustworthiness of the observed results.
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  • [1] Abdeljawad T.(2019)Solutions of the nonlinear integral equation and fractional differential equation using the technique of a fixed point with a numerical experiment in extended b-metric space Symmetry 11 7-11
  • [2] Agarwal R.P.(2020)A discussion on the existence of positive solutions of the boundary value problems via Adv. Differ. Equ. 2020 607-623
  • [3] Karapınar E.(2020)-Hilfer fractional derivative on b-metric spaces Adv. Differ. Equ. 2020 1191-1204
  • [4] Kumari P.S.(2019)On weighted Atangana–Baleanu fractional operators Chaos Solitons Fractals 126 131-143
  • [5] Afshari H.(2019)Fundamental results on weighted Caputo–Fabrizio fractional derivative Dyn. Syst. Appl. 28 13-23
  • [6] Karapınar E.(2001)Uniqueness of solutions to initial value problem of fractional differential equations of variable-order J. Korean Math. Soc. 38 1133-1144
  • [7] Al-Refai M.(1980)Hadamard-type fractional calculus Comment. Math. Univ. Carol. 21 3413-3442
  • [8] Al-Refai M.(2001)On measures of noncompactness in Banach spaces Ann. Soc. Math. Pol., 1 Comment. Math. 41 709-722
  • [9] Jarrah A.M.(2019)Measures of noncompactness related to monotonicity AIMS Math. 4 2607-2619
  • [10] An J.(2003)Lie symmetry analysis of conformable differential equations Int. J. Math. Math. Sci. 54 860-865
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