We investigate the existence of solutions for a nonlinear fractional differential inclusion in sense hybrid Caputo-proportional derivatives (HCPFDs) Banach spaces. The main result is discussed by using set-valued concern from Mönch fixed-point theorem along with Kuratowski measure noncompactness. present an example to demonstrate theoretical findings.

In this study, we develop a theory for the nonlocal hybrid boundary value problem fractional integro-differential equations featuring Atangana–Baleanu derivatives. The corresponding integral equation is presented. Then, establish existence results using Dhage’s fixed point theorem sum of three operators. We also offer additional exceptional cases and similar outcomes. order to demonstrate verif...

there are many situations for statistical process in which we have both random and vagueinformation. when uncertainty is due to fuzziness of information, fuzzy statistical control charts play animportant role in the monitoring process, because they simultaneously deal with both kinds of uncertainty.dealing with fuzzy characteristics using classical methods may cause the loss of information and ...

Accurate medical diagnosis requires a segmentation of large number of medical images. The automatic segmentation is still challenging because of low image contrast and ill-defined boundaries. Image segmentation refers to the process that partitions an image into mutually exclusive regions that cover the image. Among the various image segmentation techniques, traditional image segmentation metho...

n this paper, at first the  concept of caputo fractionalderivative is generalized on time scales. then the fractional orderdifferential equations are introduced on time scales. finally,sufficient and necessary conditions are presented for the existenceand uniqueness of solution of initial valueproblem including fractional order differential equations.

this paper studies the existence of solutions for acoupled system of nonlinear fractional differential equations. newexistence and uniqueness results are established using banach fixedpoint theorem. other existence results are obtained using schaeferand krasnoselskii fixed point theorems. some illustrative examplesare also presented.