Work on some Fractional deferential equation of variable order

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1 Preliminaries 1.1 Absolutely continuous and continuous functions: 1.2 Properties of real analysis: 1.3 Some elements of topology: 1.4 Some Special Functions Gamma function: 1.4.1 Beta function: 1.4.2 Mittag-Leffler function: 1.5 Riemann-Liouville integral with constant order. 1.6 Derivative of Riemann-Liouville with constant order : 1.7 Riemann-Liouville fractional integral of variable order : 1.8 Riemann-Liouville fractional derivative of variable order: 1.9 Generalized intervals. 1.10 Some fixed points theorems: 2 The existence of solutions Lyapunov-type inequalities to boundary value problems of variable order 2.1 Some approximation of solution 2.2 Existence result of solutions: 2.3 Example 3 Boundary value problem of weighted fractional derivative of a function with a respect to another function of variable order 3.1 Existence of Solutions 3.2 Example

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