Nonlinear Sequential Caputo and Caputo-Hadamard Fractional Differential Equations with Dirichlet Boundary Conditions in Banach Spaces

Abstract

This paper is devoted to the existence of solutions for certain classes of nonlinear sequential Caputo and Caputo-Hadamard fractional differential equations with Dirichlet boundary conditions in Banach spaces. Moreover, our analysis is based on Darbo’s fixed point theorem in conjunction with the technique of Hausdorff measure of noncompactness. An example is also presented to illustrate the effectiveness of the main results.

On Generalized Proportional Fractional Order Derivatives and Darboux Problem for Partial Differential Equations

“…By allowing for the diferentiation and integration of noninteger orders, fractional calculus is able to ofer greater accuracy and fexibility in the study of various phenomena and has a wide range of applications (see [1][2][3][4]). Ordinary and partial fractional diferential equations have developed signifcantly in recent years (see [5][6][7][8][9]).…”

Some Results on Fractional Boundary Value Problem for Caputo-Hadamard Fractional Impulsive Integro Differential Equations

“…Using the fixed-point theorem (FPT), existence and uniqueness results (E-UR) have been developed. Recently, it has been noted that many of the materials on the subject focus on FDEs of the Caputo and Riemann-Liouville types with various situations, including time delays, impulses, and boundary value conditions (BVC) [5,10,[13][14][15][16][17][18][19][20][21][22][23][24][25].…”

“…We extend the C-HFD, nonlinear integral terms, and impulsive conditions to the results discussed in [25].…”