Existence Results for Caputo–Hadamard Nonlocal Fractional Multi-Order Boundary Value Problems

Abstract

In this paper, we studied the existence results for solutions of a new class of the fractional boundary value problem in the Caputo–Hadamard settings. Moreover, boundary conditions of this fractional problem were formulated as the mixed multi-order Hadamard integro-derivative conditions. To prove the main existence results, we applied two well-known techniques in the topological degree and fixed point theories. Finally, we provide two examples to show the compatibility of our theoretical findings.

On solutions of nonlinear BVPs with general boundary conditions by using a generalized Riesz–Caputo operator

“…2 Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia. 3 Group of Mathematics, Faculty of Engineering, Ostim Technical University, Ankara, 06374, Turkey. 4 Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.…”

“…As we know, the existence theory is meat-and-potatoes in every field of science, as it is very applicative to comprehend whether there is a solution to a given differential equation beforehand; otherwise, all the attempts to find a numerical or analytic solution will become valueless. The analysis of fractional differential equations has been carried out by various authors (see, for example, [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]).…”

Existence and Ulam stability of solutions for Caputo-Hadamard fractional differential equations

“…The existence and uniqueness of mild solutions of boundary value problem for Caputo-Hadamard fractional differential equations with integral and anti-periodic conditions investigated by [20]. Rezapour et al [35] investigated the existence results for solutions of a new class of the fractional boundary value problem in the Caputo-Hadamard settings. Abbas et al [2] proved some existence results for a class of Caputo-Hadamard fractional differential equations, the results are based on M önch's fixed point theorem associated with the technique of measure of non-compactness.…”

Existence and H-U Stability of Solution for Coupled System of Fractional-Order with Integral Conditions Involving Caputo-Hadamard Derivatives, Hadamard Integrals

“…where t ∈ ½1, e, ρ, ϖ ∈ ð3, 4, δ ∈ ð1, 2, κ ∈ ð0, 1, and μ, ϑ > 0 with δ + ϑ ≠ 0 and also α, β ∈ ℝ. In 2021, Rezapour et al [36] investigated Caputo-Hadamard fractional boundary value problem via mixed multi-order integro-derivative conditions:…”