Trigger SynchronizeWithJIRAIssue on Case (after update) {
if (JIRA.currentUserIsNotJiraAgent()) {
    if(System.isFuture() == false || System.isBatch() == false || System.isScheduled() == false) { //Check, If Not in any Async Apex context, only then execute the Future Method.
       system.debug('System.isFuture()---->'+System.isFuture());
       system.debug('System.isBatch()--->'+System.isBatch());
       system.debug('System.isScheduled()--->'+System.isScheduled());
       system.debug('entering@@@@@@@@');
       system.debug('@@@@JIRA.currentUserIsNotJiraAgent()@@@@----->'+JIRA.currentUserIsNotJiraAgent());
        for (Case c : Trigger.new) {
            String objectType ='Case'; //Please change this according to the object type
            String objectId = c.Id;
            JIRAConnectorWebserviceCalloutSync.synchronizeWithJIRAIssue(JIRA.baseUrl, JIRA.systemId, objectType, objectId);
        }
    }
}

global class JIRAConnectorWebserviceCalloutSync {
@future (callout=true)
WebService static void synchronizeWithJIRAIssue(String baseUrl, String systemId, String objectType, String caseId) {
system.debug('baseurl@@@@@----->'+baseUrl+'systemId@@@---->'+systemId+'objectType@@@@--->'+objectType+'casid@@@@---->'+caseId);
    try {
        HttpRequest req = buildRequest(baseUrl, JIRA.username, JIRA.password, systemId, objectType, caseId);
        JIRA.sendRequest(req);
    } catch(System.CalloutException e) {
        System.debug(e);
    }
}

// Constructs request needed to synchronize a JIRA issue from provided parameters.
public static HttpRequest buildRequest(String baseUrl, String username, String password,
                                       String systemId, String objectType, String caseId) {
    HttpRequest req = new HttpRequest();
    String basicAuthHeader = JIRA.authHeader(username, password);
    String endpoint = getEndpoint(baseUrl, systemId, objectType, caseId);
    system.debug('end point @@@@@------>'+endpoint);
    system.debug('basicAuthHeader@@@@----->'+basicAuthHeader);
    req.setHeader('Authorization', basicAuthHeader);
    req.setHeader('Content-Type', 'application/json');
    req.setHeader('Content-Length', '0');
    req.setEndpoint(endpoint);
    req.setMethod('PUT');
    return req;
}

// Creates the endpoint to synchronize the issue from provided parameters.
private static String getEndpoint(String baseUrl, String systemId, String objectType, String caseId) {
    return baseUrl + '/rest/customware/connector/1.0/' + systemId + '/' + objectType +  '/' + caseId + '/issue/synchronize.json';
}